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Popular >

derivative of cos^2(x^3)

Solution

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

Solution

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

Solution steps

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

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})

Graph

Popular Examples

integral from 0 to x of sqrt(1+x^2)

\int_{0}^{x} 1 + x^{2} d x

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\frac{\partial}{\partial y} (x^{2} y + y^{2} z + x z^{2})

derivative of f(x)=(6x-1)/(x^3)derivative of

f (x) = \frac{6 x - 1}{x ^{3}}

integral from 3 to 5 of x^3

\int_{3}^{5} x^{3} d x

integral from 0 to 3 of 1/(x-2)

\int_{0}^{3} \frac{1}{x - 2} d x

Frequently Asked Questions (FAQ)

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