What is the derivative of cos^2(x^7) ?

The derivative of cos^2(x^7) is -14x^6cos(x^7)sin(x^7)

What is the first derivative of cos^2(x^7) ?

The first derivative of cos^2(x^7) is -14x^6cos(x^7)sin(x^7)

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

- 14 x^{6} cos (x^{7}) sin (x^{7})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x^{7})) = - sin (x^{7}) \cdot 7 x^{6}

= 2 cos (x^{7}) (- sin (x^{7}) \cdot 7 x^{6})

Simplify

= - 14 x^{6} cos (x^{7}) sin (x^{7})

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What is the derivative of cos^2(x^7) ?
The derivative of cos^2(x^7) is -14x^6cos(x^7)sin(x^7)
What is the first derivative of cos^2(x^7) ?
The first derivative of cos^2(x^7) is -14x^6cos(x^7)sin(x^7)