What is the derivative of f(x)=cos^6(x) ?

The derivative of f(x)=cos^6(x) is -6cos^5(x)sin(x)

What is the first derivative of f(x)=cos^6(x) ?

The first derivative of f(x)=cos^6(x) is -6cos^5(x)sin(x)

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derivative of

f (x) = cos^{6} (x)

- 6 cos^{5} (x) sin (x)

Solution steps

\frac{d}{d x} (cos^{6} (x))

Apply the chain rule:

6 (cos (x))^{5} \frac{d}{d x} (cos (x))

= 6 (cos (x))^{5} \frac{d}{d x} (cos (x))

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

= 6 (cos (x))^{5} (- sin (x))

Simplify

= - 6 cos^{5} (x) sin (x)

What is the derivative of f(x)=cos^6(x) ?
The derivative of f(x)=cos^6(x) is -6cos^5(x)sin(x)
What is the first derivative of f(x)=cos^6(x) ?
The first derivative of f(x)=cos^6(x) is -6cos^5(x)sin(x)