What is the derivative of cos^5(x) ?

The derivative of cos^5(x) is -5cos^4(x)sin(x)

What is the first derivative of cos^5(x) ?

The first derivative of cos^5(x) is -5cos^4(x)sin(x)

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derivative of

cos^{5} (x)

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

Solution steps

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

Apply the chain rule:

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

= 5 (cos (x))^{4} \frac{d}{d x} (cos (x))

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

= 5 (cos (x))^{4} (- sin (x))

Simplify

= - 5 cos^{4} (x) sin (x)

x \to 0 lim (\frac{x - 1}{3 x - 1})

\frac{d}{d x} (\frac{7}{3} x^{3} - 2 x^{2} + 10)

\int \frac{12 x + 30}{( x ^{2} + 2 x - 8 )} d x

\frac{\partial}{\partial y} (x^{3} + 3 x^{2} y - y^{4})

\int \frac{2}{x ^{2} + 8 x + 17} d x

What is the derivative of cos^5(x) ?
The derivative of cos^5(x) is -5cos^4(x)sin(x)
What is the first derivative of cos^5(x) ?
The first derivative of cos^5(x) is -5cos^4(x)sin(x)