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})

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derivative of

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

- 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})

y = x^{2} - x + 7

\frac{d x}{d t} = 3 x t^{2} - 3 t^{2}

\int_{0}^{l n (5)} e^{x} - e^{- 3 x} d x

\frac{x}{4 x + 6}

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})