en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sec^4(x-tan^4(x))

Solution

\frac{d}{d x} (sec^{4} (x) - tan^{4} (x))

Solution

4 sec^{2} (x) tan (x)

Solution steps

\frac{d}{d x} (sec^{4} (x) - tan^{4} (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sec^{4} (x)) - \frac{d}{d x} (tan^{4} (x))

\frac{d}{d x} (sec^{4} (x)) = 4 sec^{4} (x) tan (x)

\frac{d}{d x} (tan^{4} (x)) = 4 tan^{3} (x) sec^{2} (x)

= 4 sec^{4} (x) tan (x) - 4 tan^{3} (x) sec^{2} (x)

Simplify

4 sec^{4} (x) tan (x) - 4 tan^{3} (x) sec^{2} (x) : 4 sec^{2} (x) tan (x)

= 4 sec^{2} (x) tan (x)

Popular Examples

y^{^{'}} = 3 - (2 y)

(\partial)/(\partial y)(ln(x^2+y^3))

\frac{\partial}{\partial y} (ln (x^{2} + y^{3}))

simplify (x-5)/(sqrt(x))simplify

\frac{x - 5}{x}

derivative of (1+2xsqrt(y))

\frac{d}{d x} ((1 + 2 x) y)

integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2}

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} + \frac{1}{2} y^{- \frac{1}{2}} d y

Frequently Asked Questions (FAQ)

What is the derivative of sec^4(x-tan^4(x)) ?
The derivative of sec^4(x-tan^4(x)) is 4sec^2(x)tan(x)
What is the first derivative of sec^4(x-tan^4(x)) ?
The first derivative of sec^4(x-tan^4(x)) is 4sec^2(x)tan(x)