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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derivative of

(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}

t \to π lim (- 2 sin (- \frac{t}{2}))

\int_{0}^{\infty} a f (x) d x

x \to 2 + lim (ln ∣ x - 2 ∣)

f (x) = 7 x - 3 x^{2}

\int \frac{1}{x ^{2} - 49} d x

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