What is the derivative of cos(2xe^{2x}) ?

The derivative of cos(2xe^{2x}) is -2e^{2x}sin(2x)+2e^{2x}cos(2x)

What is the first derivative of cos(2xe^{2x}) ?

The first derivative of cos(2xe^{2x}) is -2e^{2x}sin(2x)+2e^{2x}cos(2x)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (2 x), g = e^{2 x}

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

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

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

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

Simplify

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

What is the derivative of cos(2xe^{2x}) ?
The derivative of cos(2xe^{2x}) is -2e^{2x}sin(2x)+2e^{2x}cos(2x)
What is the first derivative of cos(2xe^{2x}) ?
The first derivative of cos(2xe^{2x}) is -2e^{2x}sin(2x)+2e^{2x}cos(2x)