What is the derivative of f(x)=(1+cos^2(x))^7 ?

The derivative of f(x)=(1+cos^2(x))^7 is -7sin(2x)(1+cos^2(x))^6

What is the first derivative of f(x)=(1+cos^2(x))^7 ?

The first derivative of f(x)=(1+cos^2(x))^7 is -7sin(2x)(1+cos^2(x))^6

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derivative of

f (x) = (1 + cos^{2} (x))^{7}

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

Solution steps

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

Apply the chain rule:

7 (1 + cos^{2} (x))^{6} \frac{d}{d x} (1 + cos^{2} (x))

= 7 (1 + cos^{2} (x))^{6} \frac{d}{d x} (1 + cos^{2} (x))

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

= 7 (1 + cos^{2} (x))^{6} (- sin (2 x))

Simplify

= - 7 sin (2 x) (1 + cos^{2} (x))^{6}

\int \frac{1}{2 sin ( θ )} d θ

\frac{\partial ^{2}}{\partial u ( v ) \partial v} (8 v e^{- 6 u (v)})

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\frac{16 x}{x ^{2} + 16}

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What is the derivative of f(x)=(1+cos^2(x))^7 ?
The derivative of f(x)=(1+cos^2(x))^7 is -7sin(2x)(1+cos^2(x))^6
What is the first derivative of f(x)=(1+cos^2(x))^7 ?
The first derivative of f(x)=(1+cos^2(x))^7 is -7sin(2x)(1+cos^2(x))^6