Upgrade to Pro Continue to site
We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

  • Solutions
    Integral Calculator Derivative Calculator Algebra Calculator Matrix Calculator More...
  • Graphing
    Line Graph Calculator Exponential Graph Calculator Quadratic Graph Calculator Sine Graph Calculator More...
  • Calculators
    BMI Calculator Compound Interest Calculator Percentage Calculator Acceleration Calculator More...
  • Geometry
    Pythagorean Theorem Calculator Circle Area Calculator Isosceles Triangle Calculator Triangles Calculator More...
  • Tools
    Notebook Groups Cheat Sheets Worksheets Study Guides Practice Verify Solution
    • en
    English Español Português Français Deutsch Italiano Русский 中文(简体) 한국어 日本語 Tiếng Việt עברית العربية
  • Upgrade
Good job!
Practice Practice More
Type your Answer
Enter a problem
x2 x□ log□ √☐ □√☐ ≤ ≥ □□  · ÷ x◦ π
(☐)′ ddx  ∂∂x  ∫ ∫□□ lim ∑ ∞ θ (f ◦ g) f(x)
▭ |▭ ×▭▭ +▭▭ −▭▭ ( ) × ☐☐☐ 
Take a challenge
Subscribe to verify your answer
Subscribe
Are you sure you want to leave this Challenge? By closing this window you will lose this challenge
Cancel
Leave
  • Pre Algebra
    Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
  • Algebra
    Equations Inequalities System of Equations System of Inequalities Testing Solutions Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Prove That Logical Sets Word Problems
  • Pre Calculus
    Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Trigonometry
  • Calculus
    Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
  • Functions
    Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
  • Linear Algebra
    Matrices Vectors
  • Trigonometry
    Quadrant Coterminal Angle Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
  • Statistics
    Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
  • Physics
    Mechanics
  • Chemistry
    Chemical Reactions Chemical Properties
  • Finance
    Simple Interest Compound Interest Present Value Future Value
  • Economics
    Point of Diminishing Return
  • Conversions
    Currency Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Degrees Minutes Seconds Hexadecimal Scientific Notation Distance Weight Time Volume
 
Solutions > EN: multivariable-implicit-derivative-calculator title >

implicit derivative of (dy)/(dx),x=sec(1/y)

Topic
  • Pre Algebra
  • Algebra
  • Pre Calculus
  • Calculus
  • Derivatives
    • First Derivative
    • WRT
    • Specify Method
      • Chain Rule
      • Product Rule
      • Quotient Rule
      • Sum/Diff Rule
    • Second Derivative
    • Third Derivative
    • Higher Order Derivatives
    • Derivative at a point
    • Partial Derivative
    • Implicit Derivative
    • Second Implicit Derivative
    • Derivative using Definition
  • Derivative Applications
    • Tangent
    • Slope of Tangent
    • Normal
    • Curved Line Slope
    • Extreme Points
    • Tangent to Conic
    • Linear Approximation
    • Difference Quotient
    • Horizontal Tangent
  • Limits
    • One Variable
    • Multi Variable Limit
    • One Sided
    • At Infinity
    • Specify Method
      • L'Hopital's Rule
      • Squeeze Theorem
      • Chain Rule
      • Factoring
      • Substitution
      • Sandwich Theorem
  • Integrals
    • Indefinite Integrals
    • Definite Integrals
    • Specific-Method
      • Partial Fractions
      • U-Substitution
      • Trigonometric Substitution
      • Weierstrass Substitution
      • By Parts
      • Long Division
    • Improper Integrals
    • Antiderivatives
    • Double Integrals
    • Triple Integrals
    • Multiple Integrals
  • Integral Applications
    • Limit of Sum
    • Area under curve
    • Area between curves
    • Area under polar curve
    • Volume of solid of revolution
    • Arc Length
    • Function Average
  • Integral Approximation
    • Riemann Sum
    • Trapezoidal
    • Simpson's Rule
    • Midpoint Rule
  • Series
    • Convergence
      • Geometric Series Test
      • Telescoping Series Test
      • Alternating Series Test
      • P Series Test
      • Divergence Test
      • Ratio Test
      • Root Test
      • Comparison Test
      • Limit Comparison Test
      • Integral Test
    • Absolute Convergence
    • Power Series
      • Radius of Convergence
      • Interval of Convergence
  • ODE
    • Linear First Order
    • Linear w/constant coefficients
    • Separable
    • Bernoulli
    • Exact
    • Second Order
    • Homogenous
    • Non Homogenous
    • Substitution
    • System of ODEs
    • IVP using Laplace
    • Series Solutions
    • Method of Frobenius
    • Gamma Function
  • Multivariable Calculus
    • Partial Derivative
    • Implicit Derivative
    • Tangent to Conic
    • Multi Variable Limit
    • Multiple Integrals
    • Gradient
    • Divergence
    • Extreme Points
  • Laplace Transform
    • Inverse
  • Taylor/Maclaurin Series
    • Taylor Series
    • Maclaurin Series
  • Fourier Series
  • Fourier Transform
  • Functions
  • Linear Algebra
  • Trigonometry
  • Statistics
  • Physics
  • Chemistry
  • Finance
  • Economics
  • Conversions
Full pad
x2 x□ log□ √☐ □√☐ ≤ ≥ □□  · ÷ x◦ π
(☐)′ ddx  ∂∂x  ∫ ∫□□ lim ∑ ∞ θ (f ◦ g) f(x)
−▭▭ < 7 8 9 ÷ AC
+▭▭ > 4 5 6 × ☐☐☐ 
×▭▭ ( 1 2 3 − x
▭ |▭ ) . 0 = + y
Basic αβγ ABΓ sincos ≥÷→ x ℂ∀ ∑ ∫ ∏ (
☐☐
☐☐
)		 H2O
☐2 x☐ √☐ □√☐ □□  log□ π θ ∞ ∫ ddx 
≥ ≤ · ÷ x◦ (☐) |☐| (f ◦ g) f(x) ln e☐
(☐)′ ∂∂x  ∫□□ lim ∑ sin cos tan cot csc sec
α β γ δ ζ η θ ι κ λ μ
ν ξ π ρ σ τ υ ϕ χ ψ ω
A B Γ Δ E Z H Θ K Λ M
N Ξ Π P Σ T ϒ Φ X Ψ Ω
sin cos tan cot sec csc sinh cosh tanh coth sech
arcsin arccos arctan arccot arcsec arccsc arcsinh arccosh arctanh arccoth arcsech
{
☐
☐
 		 {
☐
☐
☐
 		 = ≠ ÷ · × < > ≤ ≥
(☐) [☐] ▭ |▭ ×▭▭ +▭▭ −▭▭ ☐! x◦ → ⌊☐⌋ ⌈☐⌉
☐ ⃗ ☐ ∈ ∀ ∉ ∃ ℝ ℂ ℕ ℤ ∅
∨ ∧ ¬ ⊕ ∩ ∪ ☐c ⊂ ⊆ ⊃ ⊇
∫ ∫∫ ∫∫∫ ∫☐☐ ∫☐☐∫☐☐ ∫☐☐∫☐☐∫☐☐ ∑ ∏
lim limx→∞ limx→0+ limx→0− ddx  d2dx2  (☐)′ (☐)′′ ∂∂x 
(2×2) (2×3) (3×3) (3×2) (4×2) (4×3) (4×4) (3×4) (2×4) (5×5) matrix button
(1×2) (1×3) (1×4) (1×5) (1×6) (2×1) (3×1) (4×1) (5×1) (6×1) (7×1)
Radians Degrees ☐! ( ) % clear
arcsin sin √☐ 7 8 9 ÷
arccos cos ln 4 5 6 ×
arctan tan log 1 2 3 −
π e x☐ 0 . = +
implicit derivative tangent volume laplace fourier
See All
area
asymptotes
critical points
derivative
domain
eigenvalues
eigenvectors
expand
extreme points
factor
implicit derivative
inflection points
intercepts
inverse
laplace
inverse laplace
partial fractions
range
slope
simplify
solve for
tangent
taylor
vertex
geometric test
alternating test
telescoping test
pseries test
root test
implicit derivative dydx , x=sec(1y )
Steps Graph Related Examples
Generated by AI
AI explanations are generated using OpenAI technology. AI generated content may present inaccurate or offensive content that does not represent Symbolab's view.
Verify your Answer
Subscribe to verify your answer
Subscribe
Save to Notebook!
Sign in to save notes
Sign in
implicit derivative dydx , x=sec(1y )
 
Verify
Save

Solution

dydx =−y2sec(1y )tan(1y ) 
 
Show Steps
 
Hide Steps
 

Number Line

Related
  • implicit derivative $$\frac{dy}{dx},\:x^{2}\left(x-y\right)^{2}=x^{2}-y^{2}$$
  • implicit derivative $$\frac{dy}{dx},\:x^{8}-y^{7}=9$$
  • implicit derivative $$\frac{dy}{dx},\:x^{6}-y^{9}=10xy$$
Implicit Derivative Examples
  • implicit derivative dydx , (x−y)2=x+y−1
  • implicit derivative dydx , x3+y3=4
  • implicit derivative dxdy , x3+y3=4
  • implicit derivative dydx , y=sin(3x+4y)
  • implicit derivative exy=e4x−e5y
  • implicit derivative dxdy , exy=e4x−e5y
Description
Implicit differentiation solver step-by-step

multivariable-implicit-derivative-calculator

implicit derivative $$\frac{dy}{dx},x=\sec\left(\frac{1}{y}\right)$$

en

Related Symbolab blog posts
  • High School Math Solutions – Derivative Calculator, Trigonometric Functions
    In the previous posts we covered the basic algebraic derivative rules (click here to see previous post). But how...
    • Popular topics
    median calculator dot product calculator arc length calculator maclaurin series calculator z score calculator critical point calculator inequalities calculator range calculator determinant calculator second derivative calculator lcm calculator partial derivative calculator complete the square calculator distributive property calculator mixed fractions calculator Time Calculator gradient calculator triple integrals calculator partial fractions calculator indefinite integral calculator solve for x calculator double integral solver vector calculator Date Calculator vertex calculator binomial expansion calculator decimal to fraction calculator difference quotient calculator eigenvalue calculator piecewise functions calculator radius of convergence calculator roots calculator exponential function calculator interval of convergence calculator fractions divide calculator inflection point calculator expand calculator variance calculator fractions multiply calculator fourier series calculator foil calculator modulo calculator series convergence calculator linear algebra calculator
    Chat with Symbo
    AI may present inaccurate or offensive content that does not represent Symbolab's views.
    Do not enter any personal information
    Enter a problem
    Cooking Calculators
    Cooking Measurement Converter Cooking Ingredient Converter Cake Pan Converter More calculators
    Fitness Calculators
    BMI Calculator Calorie Calculator BMR Calculator More calculators
    Save to Notebook!
    Sign in
    Notebook
      View Full Notebook
      Study Tools AI Math Solver Popular Problems Worksheets Study Guides Practice Cheat Sheets Calculators Graphing Calculator Geometry Calculator Verify Solution
      Apps Symbolab App (Android) Graphing Calculator (Android) Practice (Android) Symbolab App (iOS) Graphing Calculator (iOS) Practice (iOS) Chrome Extension Symbolab Math Solver API
      Company About Symbolab Blog Help Contact Us
      Legal Privacy Terms Cookie Policy Cookie Settings Copyright, Community Guidelines, DSA & other Legal Resources Learneo Legal Center
      Feedback Social Media
      Symbolab, a Learneo, Inc. business
      © Learneo, Inc. 2024
      (optional)
      (optional)

      Please add a message.

      Message received. Thanks for the feedback.

      Cancel Send