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

The derivative of 3e^{3x}cos(2x-2e^{3x}sin(2x)) is 5e^{3x}cos(2x)-12e^{3x}sin(2x)

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

The first derivative of 3e^{3x}cos(2x-2e^{3x}sin(2x)) is 5e^{3x}cos(2x)-12e^{3x}sin(2x)

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\frac{d}{d x} (3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x))

5 e^{3 x} cos (2 x) - 12 e^{3 x} sin (2 x)

Solution steps

\frac{d}{d x} (3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 e^{3 x} cos (2 x)) - \frac{d}{d x} (2 e^{3 x} sin (2 x))

\frac{d}{d x} (3 e^{3 x} cos (2 x)) = 3 (3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x))

\frac{d}{d x} (2 e^{3 x} sin (2 x)) = 2 (e^{3 x} \cdot 3 sin (2 x) + cos (2 x) \cdot 2 e^{3 x})

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

Simplify

3 (3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x)) - 2 (e^{3 x} \cdot 3 sin (2 x) + cos (2 x) \cdot 2 e^{3 x}) : 5 e^{3 x} cos (2 x) - 12 e^{3 x} sin (2 x)

= 5 e^{3 x} cos (2 x) - 12 e^{3 x} sin (2 x)

x^{2} d x + y (x - 1) d y = 0

4 + x^{6}

x e^{x^{2}}

\int 6 x^{- 7} d x

f (x) = (1 + 4 x^{2}) (x - x^{2})

What is the derivative of 3e^{3x}cos(2x-2e^{3x}sin(2x)) ?
The derivative of 3e^{3x}cos(2x-2e^{3x}sin(2x)) is 5e^{3x}cos(2x)-12e^{3x}sin(2x)
What is the first derivative of 3e^{3x}cos(2x-2e^{3x}sin(2x)) ?
The first derivative of 3e^{3x}cos(2x-2e^{3x}sin(2x)) is 5e^{3x}cos(2x)-12e^{3x}sin(2x)