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

The derivative of cos^4(x+sin^4(x)) is -4cos(x)sin(x)cos(2x)

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

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

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

- 4 cos (x) sin (x) cos (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - 4 cos^{3} (x) sin (x) + 4 sin^{3} (x) cos (x)

Simplify

- 4 cos^{3} (x) sin (x) + 4 sin^{3} (x) cos (x) : - 4 cos (x) sin (x) cos (2 x)

= - 4 cos (x) sin (x) cos (2 x)

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