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

The derivative of e^{2x}(2cos(3x+3sin(3x))) is 13e^{2x}cos(3x)

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

The first derivative of e^{2x}(2cos(3x+3sin(3x))) is 13e^{2x}cos(3x)

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

13 e^{2 x} cos (3 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (2 cos (3 x) + 3 sin (3 x)) = - 6 sin (3 x) + 9 cos (3 x)

= e^{2 x} \cdot 2 (2 cos (3 x) + 3 sin (3 x)) + (- 6 sin (3 x) + 9 cos (3 x)) e^{2 x}

Simplify

e^{2 x} \cdot 2 (2 cos (3 x) + 3 sin (3 x)) + (- 6 sin (3 x) + 9 cos (3 x)) e^{2 x} : 13 e^{2 x} cos (3 x)

= 13 e^{2 x} cos (3 x)

\int_{- 1}^{1} ∣ x ∣ d x

f (x) = e^{a r c t a n (2 t^{2})}

\int x^{2} (2 x^{3} + 3)^{4} d x

\int \frac{x + 9}{9 - 3 x - 2 x ^{2}} d x

x \to 0 lim ((1 + \frac{3}{x ^{2}})^{x})

What is the derivative of e^{2x}(2cos(3x+3sin(3x))) ?
The derivative of e^{2x}(2cos(3x+3sin(3x))) is 13e^{2x}cos(3x)
What is the first derivative of e^{2x}(2cos(3x+3sin(3x))) ?
The first derivative of e^{2x}(2cos(3x+3sin(3x))) is 13e^{2x}cos(3x)