What is the derivative of (cos(x^3)^2) ?

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

What is the first derivative of (cos(x^3)^2) ?

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

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\frac{d}{d x} ((cos (x^{3}))^{2})

- 3 x^{2} sin (2 x^{3})

Solution steps

\frac{d}{d x} ((cos (x^{3}))^{2})

Apply the chain rule:

2 cos (x^{3}) \frac{d}{d x} (cos (x^{3}))

= 2 cos (x^{3}) \frac{d}{d x} (cos (x^{3}))

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

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

Simplify

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

= - 3 x^{2} sin (2 x^{3})

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