(\partial)/(\partial x)((x-3)/(xt+16))

Topic

Full pad

`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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

Steps Examples

Generated by AI

inverse laplace 2x²−36 −1x²+6x

Solution

e^6t−H(t)6

Show Steps

Hide Steps

Solution steps

One step at a time

L⁻¹{2x²−36 −1x²+6x }

Take the partial fraction of 2x²−36 : −16(x+6) +16(x−6)

=L⁻¹{−16(x+6) +16(x−6) −1x²+6x }

Take the partial fraction of 1x²+6x : 16x −16(x+6)

=L⁻¹{−16(x+6) +16(x−6) −16x +16(x+6) }

Use the linearity property of Inverse Laplace Transform:
For functions f(s), g(s) and constants a, b: L⁻¹{a·f(s)+b·g(s)}=a·L⁻¹{f(s)}+b·L⁻¹{g(s)}

=−L⁻¹{16(x+6) }+L⁻¹{16(x−6) }−L⁻¹{16x }+L⁻¹{16(x+6) }

L⁻¹{16(x+6) }: 16 e^−6t

L⁻¹{16(x−6) }: 16 e^6t

L⁻¹{16x }: 16 H(t)

=−16 e^−6t+16 e^6t−16 H(t)+16 e^−6t

Simplify −16 e^−6t+16 e^6t−16 H(t)+16 e^−6t: e^6t−H(t)6

=e^6t−H(t)6

Description

The Derivative Calculator is an invaluable online tool designed to compute derivatives efficiently, aiding students, educators, and professionals alike. Here's how to utilize its capabilities:

Begin by entering your mathematical function into the above input field, or scanning it with your camera.
Click the 'Go' button to instantly generate the derivative of the input function.
The calculator provides detailed step-by-step solutions, facilitating a deeper understanding of the derivative process.

Derivative Examples

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

Hi, ask a question about inverse laplace 2x²−36 −1x²+6x

Cooking Calculators

Cooking Measurement Converter Cooking Ingredient Converter Cake Pan Converter More calculators

Fitness Calculators

BMI Calculator Calorie Calculator BMR Calculator More calculators

Notebook

View Full Notebook

−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

(\partial)/(\partial x)((x-3)/(xt+16))

Solution

Solution steps

Number Line