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

The derivative of cos^3(x^2) is -6xcos^2(x^2)sin(x^2)

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

The first derivative of cos^3(x^2) is -6xcos^2(x^2)sin(x^2)

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

- 6 x cos^{2} (x^{2}) sin (x^{2})

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{2 x}

y = \frac{4}{x}, (- 5, - \frac{4}{5})

7 x y \frac{d y}{d x} = 1

(- 5, - 7), (4, - 1)

x, at x = 81

What is the derivative of cos^3(x^2) ?
The derivative of cos^3(x^2) is -6xcos^2(x^2)sin(x^2)
What is the first derivative of cos^3(x^2) ?
The first derivative of cos^3(x^2) is -6xcos^2(x^2)sin(x^2)