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

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

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

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

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

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

Solution steps

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

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 (arcsin (x))

\frac{d}{d x} (lo g_{2} (x^{2} - 9 x))

\frac{d}{d x} ((x^{2} - 1) (x^{2} - 4) (x^{2} - 9))

\frac{\partial}{\partial x} (50 - (4 x^{2} + y^{2}))

\frac{d}{d x} (1 - cos (x))

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