What is the derivative of (1+cos^2(x))^9 ?

The derivative of (1+cos^2(x))^9 is -9sin(2x)(1+cos^2(x))^8

What is the first derivative of (1+cos^2(x))^9 ?

The first derivative of (1+cos^2(x))^9 is -9sin(2x)(1+cos^2(x))^8

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derivative of

(1 + cos^{2} (x))^{9}

- 9 sin (2 x) (1 + cos^{2} (x))^{8}

Solution steps

\frac{d}{d x} ((1 + cos^{2} (x))^{9})

Apply the chain rule:

9 (1 + cos^{2} (x))^{8} \frac{d}{d x} (1 + cos^{2} (x))

= 9 (1 + cos^{2} (x))^{8} \frac{d}{d x} (1 + cos^{2} (x))

\frac{d}{d x} (1 + cos^{2} (x)) = - sin (2 x)

= 9 (1 + cos^{2} (x))^{8} (- sin (2 x))

Simplify

= - 9 sin (2 x) (1 + cos^{2} (x))^{8}

What is the derivative of (1+cos^2(x))^9 ?
The derivative of (1+cos^2(x))^9 is -9sin(2x)(1+cos^2(x))^8
What is the first derivative of (1+cos^2(x))^9 ?
The first derivative of (1+cos^2(x))^9 is -9sin(2x)(1+cos^2(x))^8