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

The derivative of cos^2(e^x+sqrt(x)) is -sin(2(sqrt(x)+e^x))(1/(2sqrt(x))+e^x)

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

The first derivative of cos^2(e^x+sqrt(x)) is -sin(2(sqrt(x)+e^x))(1/(2sqrt(x))+e^x)

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derivative of

cos^{2} (e^{x} + x)

- sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (e^{x} + x)) = - sin (e^{x} + x) (e^{x} + \frac{1}{2 x})

= 2 cos (e^{x} + x) (- sin (e^{x} + x) (e^{x} + \frac{1}{2 x}))

Simplify

2 cos (e^{x} + x) (- sin (e^{x} + x) (e^{x} + \frac{1}{2 x})) : - sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})

= - sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})

What is the derivative of cos^2(e^x+sqrt(x)) ?
The derivative of cos^2(e^x+sqrt(x)) is -sin(2(sqrt(x)+e^x))(1/(2sqrt(x))+e^x)
What is the first derivative of cos^2(e^x+sqrt(x)) ?
The first derivative of cos^2(e^x+sqrt(x)) is -sin(2(sqrt(x)+e^x))(1/(2sqrt(x))+e^x)