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

The derivative of 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 cos^4(sin^3(x)) ?

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

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\frac{d}{d 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)

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