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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int 2 sin^{4} (x) cos^{2} (x) d x

\frac{d}{d x} (- \frac{e ^{- 2 x^{3}}}{4 x ^{4}})

x \to - 4 lim ([x])

\int \frac{x}{4 - 2 x ^{2}} d x

\int \frac{3}{z} d z

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