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Popular Calculus >

derivative of cos^3(e^{4x})

Solution

derivative of

cos^{3} (e^{4 x})

Solution

- 12 e^{4 x} cos^{2} (e^{4 x}) sin (e^{4 x})

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

= - 12 e^{4 x} cos^{2} (e^{4 x}) sin (e^{4 x})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of cos^3(e^{4x}) ?
The derivative of cos^3(e^{4x}) is -12e^{4x}cos^2(e^{4x})sin(e^{4x})
What is the first derivative of cos^3(e^{4x}) ?
The first derivative of cos^3(e^{4x}) is -12e^{4x}cos^2(e^{4x})sin(e^{4x})