What is the derivative of (1+cos^2(x))^5 ?

The derivative of (1+cos^2(x))^5 is -5sin(2x)(1+cos^2(x))^4

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

The first derivative of (1+cos^2(x))^5 is -5sin(2x)(1+cos^2(x))^4

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derivative of

(1 + cos^{2} (x))^{5}

- 5 sin (2 x) (1 + cos^{2} (x))^{4}

Solution steps

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

Apply the chain rule:

5 (1 + cos^{2} (x))^{4} \frac{d}{d x} (1 + cos^{2} (x))

= 5 (1 + cos^{2} (x))^{4} \frac{d}{d x} (1 + cos^{2} (x))

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

= 5 (1 + cos^{2} (x))^{4} (- sin (2 x))

Simplify

= - 5 sin (2 x) (1 + cos^{2} (x))^{4}

n = 0 \sum \infty \frac{( e ^{n} )}{5}

\frac{d}{d x} (- 8 x^{3})

\int_{\frac{1}{7}}^{5} 6 x ln (7 x) d x

\frac{d}{d x} (\frac{8}{x - 3})

x \to \frac{π}{2} lim (x \cdot sec (x))

What is the derivative of (1+cos^2(x))^5 ?
The derivative of (1+cos^2(x))^5 is -5sin(2x)(1+cos^2(x))^4
What is the first derivative of (1+cos^2(x))^5 ?
The first derivative of (1+cos^2(x))^5 is -5sin(2x)(1+cos^2(x))^4