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Popular >

derivative of e^{3x}cos(4x)

Solution

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

Solution

3 e^{3 x} cos (4 x) - 4 e^{3 x} sin (4 x)

Solution steps

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

Apply the Product Rule:

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

f = e^{3 x}, g = cos (4 x)

= \frac{d}{d x} (e^{3 x}) cos (4 x) + \frac{d}{d x} (cos (4 x)) e^{3 x}

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

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

Simplify

= 3 e^{3 x} cos (4 x) - 4 e^{3 x} sin (4 x)

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Frequently Asked Questions (FAQ)

What is the derivative of e^{3x}cos(4x) ?
The derivative of e^{3x}cos(4x) is 3e^{3x}cos(4x)-4e^{3x}sin(4x)
What is the first derivative of e^{3x}cos(4x) ?
The first derivative of e^{3x}cos(4x) is 3e^{3x}cos(4x)-4e^{3x}sin(4x)