What is the derivative of (1+cos^2(x)^8) ?

The derivative of (1+cos^2(x)^8) is -8sin(2x)(1+cos^2(x))^7

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

The first derivative of (1+cos^2(x)^8) is -8sin(2x)(1+cos^2(x))^7

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

- 8 sin (2 x) (1 + cos^{2} (x))^{7}

Solution steps

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

Apply the chain rule:

8 (1 + cos^{2} (x))^{7} \frac{d}{d x} (1 + cos^{2} (x))

= 8 (1 + cos^{2} (x))^{7} \frac{d}{d x} (1 + cos^{2} (x))

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

= 8 (1 + cos^{2} (x))^{7} (- sin (2 x))

Simplify

= - 8 sin (2 x) (1 + cos^{2} (x))^{7}

\int (\frac{7 x + 3}{x}) d x

\frac{\partial}{\partial x} (ln (x) - 1)

\int sec (x) - cos (x) d x

(4, - 7), (8, - 7)

f (x) = x ln (x) - x

What is the derivative of (1+cos^2(x)^8) ?
The derivative of (1+cos^2(x)^8) is -8sin(2x)(1+cos^2(x))^7
What is the first derivative of (1+cos^2(x)^8) ?
The first derivative of (1+cos^2(x)^8) is -8sin(2x)(1+cos^2(x))^7