What is the derivative of (1+cos(x)^8) ?

The derivative of (1+cos(x)^8) is -8sin(x)(1+cos(x))^7

What is the first derivative of (1+cos(x)^8) ?

The first derivative of (1+cos(x)^8) is -8sin(x)(1+cos(x))^7

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\frac{d}{d x} ((1 + cos (x))^{8})

- 8 sin (x) (1 + cos (x))^{7}

Solution steps

\frac{d}{d x} ((1 + cos (x))^{8})

Apply the chain rule:

8 (1 + cos (x))^{7} \frac{d}{d x} (1 + cos (x))

= 8 (1 + cos (x))^{7} \frac{d}{d x} (1 + cos (x))

\frac{d}{d x} (1 + cos (x)) = - sin (x)

= 8 (1 + cos (x))^{7} (- sin (x))

Simplify

= - 8 sin (x) (1 + cos (x))^{7}

What is the derivative of (1+cos(x)^8) ?
The derivative of (1+cos(x)^8) is -8sin(x)(1+cos(x))^7
What is the first derivative of (1+cos(x)^8) ?
The first derivative of (1+cos(x)^8) is -8sin(x)(1+cos(x))^7