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

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

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

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

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derivative of

f (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}

arcsin (x)

\int_{5}^{10} a x - 10 b d x

f (x) = \frac{12}{x}, at x = - 2

\frac{d}{d z} (0)

x \to 0 lim (\frac{1}{x ^{\frac{1}{2}}})

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