What is the derivative of f(x)=cos^4(sin^3(x)) ?

The derivative of f(x)=cos^4(sin^3(x)) is -12cos^3(sin^3(x))sin^2(x)sin(sin^3(x))cos(x)

What is the first derivative of f(x)=cos^4(sin^3(x)) ?

The first derivative of f(x)=cos^4(sin^3(x)) is -12cos^3(sin^3(x))sin^2(x)sin(sin^3(x))cos(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = cos^{4} (sin^{3} (x))

- 12 cos^{3} (sin^{3} (x)) sin^{2} (x) sin (sin^{3} (x)) cos (x)

Solution steps

\frac{d}{d x} (cos^{4} (sin^{3} (x)))

Apply the chain rule:

4 (cos (sin^{3} (x)))^{3} \frac{d}{d x} (cos (sin^{3} (x)))

= 4 (cos (sin^{3} (x)))^{3} \frac{d}{d x} (cos (sin^{3} (x)))

\frac{d}{d x} (cos (sin^{3} (x))) = - sin (sin^{3} (x)) \cdot 3 sin^{2} (x) cos (x)

= 4 (cos (sin^{3} (x)))^{3} (- sin (sin^{3} (x)) \cdot 3 sin^{2} (x) cos (x))

Simplify

= - 12 cos^{3} (sin^{3} (x)) sin^{2} (x) sin (sin^{3} (x)) cos (x)

f (x) = x^{4} + 7 x^{2} - x, at x = 1

\frac{( x ^{2} + 1 )}{( x + 1 )}, 1

\frac{\partial}{\partial u} (u - uv)

\frac{2}{x ^{4}}

f (y) = y ln (1 + e^{y})

What is the derivative of f(x)=cos^4(sin^3(x)) ?
The derivative of f(x)=cos^4(sin^3(x)) is -12cos^3(sin^3(x))sin^2(x)sin(sin^3(x))cos(x)
What is the first derivative of f(x)=cos^4(sin^3(x)) ?
The first derivative of f(x)=cos^4(sin^3(x)) is -12cos^3(sin^3(x))sin^2(x)sin(sin^3(x))cos(x)