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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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