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

The derivative of 2e^{2x}cos(x-e^{2x}sin(x)) is 3e^{2x}cos(x)-4e^{2x}sin(x)

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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

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