What is the derivative of (1+cos^2(x)^6) ?

The derivative of (1+cos^2(x)^6) is -6sin(2x)(1+cos^2(x))^5

What is the first derivative of (1+cos^2(x)^6) ?

The first derivative of (1+cos^2(x)^6) is -6sin(2x)(1+cos^2(x))^5

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\frac{d}{d x} ((1 + cos^{2} (x))^{6})

- 6 sin (2 x) (1 + cos^{2} (x))^{5}

Solution steps

\frac{d}{d x} ((1 + cos^{2} (x))^{6})

Apply the chain rule:

6 (1 + cos^{2} (x))^{5} \frac{d}{d x} (1 + cos^{2} (x))

= 6 (1 + cos^{2} (x))^{5} \frac{d}{d x} (1 + cos^{2} (x))

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

= 6 (1 + cos^{2} (x))^{5} (- sin (2 x))

Simplify

= - 6 sin (2 x) (1 + cos^{2} (x))^{5}

What is the derivative of (1+cos^2(x)^6) ?
The derivative of (1+cos^2(x)^6) is -6sin(2x)(1+cos^2(x))^5
What is the first derivative of (1+cos^2(x)^6) ?
The first derivative of (1+cos^2(x)^6) is -6sin(2x)(1+cos^2(x))^5