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Popular >

derivative of cos^3(4x^2)

Solution

\frac{d}{d x} (cos^{3} (4 x^{2}))

Solution

- 24 x cos^{2} (4 x^{2}) sin (4 x^{2})

Solution steps

\frac{d}{d x} (cos^{3} (4 x^{2}))

Apply the chain rule:

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

= 3 (cos (4 x^{2}))^{2} \frac{d}{d x} (cos (4 x^{2}))

\frac{d}{d x} (cos (4 x^{2})) = - sin (4 x^{2}) \cdot 8 x

= 3 (cos (4 x^{2}))^{2} (- sin (4 x^{2}) \cdot 8 x)

Simplify

= - 24 x cos^{2} (4 x^{2}) sin (4 x^{2})

Popular Examples

derivative of ln(ax^n)

\frac{d}{d x} (ln (a x^{n}))

limit as x approaches infinity of 5^{-x}

x \to \infty lim (5^{- x})

derivative of (2t)/(4+t^2)derivative of

\frac{2 t}{4 + t ^{2}}

limit as x approaches 0 of (5x^3)/(x^3)

x \to 0 lim (\frac{5 x ^{3}}{x ^{3}})

xy^2dy=(x^3+y^3)dx

x y^{2} d y = (x^{3} + y^{3}) d x

Frequently Asked Questions (FAQ)

What is the derivative of cos^3(4x^2) ?
The derivative of cos^3(4x^2) is -24xcos^2(4x^2)sin(4x^2)
What is the first derivative of cos^3(4x^2) ?
The first derivative of cos^3(4x^2) is -24xcos^2(4x^2)sin(4x^2)