What is the derivative of y=cos^4(x) ?

The derivative of y=cos^4(x) is -4cos^3(x)sin(x)

What is the first derivative of y=cos^4(x) ?

The first derivative of y=cos^4(x) is -4cos^3(x)sin(x)

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derivative of

y = cos^{4} (x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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