What is the derivative of cos^2(x^4) ?

The derivative of cos^2(x^4) is -8x^3cos(x^4)sin(x^4)

What is the first derivative of cos^2(x^4) ?

The first derivative of cos^2(x^4) is -8x^3cos(x^4)sin(x^4)

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

- 8 x^{3} cos (x^{4}) sin (x^{4})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x^{4})) = - sin (x^{4}) \cdot 4 x^{3}

= 2 cos (x^{4}) (- sin (x^{4}) \cdot 4 x^{3})

Simplify

= - 8 x^{3} cos (x^{4}) sin (x^{4})

What is the derivative of cos^2(x^4) ?
The derivative of cos^2(x^4) is -8x^3cos(x^4)sin(x^4)
What is the first derivative of cos^2(x^4) ?
The first derivative of cos^2(x^4) is -8x^3cos(x^4)sin(x^4)