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

The derivative of cos^2(e^x) is -e^xsin(2e^x)

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

The first derivative of cos^2(e^x) is -e^xsin(2e^x)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 cos (e^{x}) (- sin (e^{x}) e^{x}) : - e^{x} sin (2 e^{x})

= - e^{x} sin (2 e^{x})

What is the derivative of cos^2(e^x) ?
The derivative of cos^2(e^x) is -e^xsin(2e^x)
What is the first derivative of cos^2(e^x) ?
The first derivative of cos^2(e^x) is -e^xsin(2e^x)