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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

f = e^{3 x}, g = - 2 sin (2 x) + 3 cos (2 x)

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d}{d x} (- 2 sin (2 x) + 3 cos (2 x)) = - 4 cos (2 x) - 6 sin (2 x)

= e^{3 x} \cdot 3 (- 2 sin (2 x) + 3 cos (2 x)) + (- 4 cos (2 x) - 6 sin (2 x)) e^{3 x}

Simplify

e^{3 x} \cdot 3 (- 2 sin (2 x) + 3 cos (2 x)) + (- 4 cos (2 x) - 6 sin (2 x)) e^{3 x} : - 12 e^{3 x} sin (2 x) + 5 e^{3 x} cos (2 x)

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

\int x^{5} + 2 x^{3} + x d x

\frac{d}{d x} (x + 60)

\int_{0}^{\infty} \frac{1}{x ^{5}} d x

\int y e^{\frac{x}{y}} d x

\int \frac{x}{12 - 9 x ^{2}} d x

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