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Popular Calculus >

derivative of e^{4x}cos(7x)

Solution

derivative of

e^{4 x} cos (7 x)

Solution

4 e^{4 x} cos (7 x) - 7 e^{4 x} sin (7 x)

Solution steps

\frac{d}{d x} (e^{4 x} cos (7 x))

Apply the Product Rule:

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

f = e^{4 x}, g = cos (7 x)

= \frac{d}{d x} (e^{4 x}) cos (7 x) + \frac{d}{d x} (cos (7 x)) e^{4 x}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

\frac{d}{d x} (cos (7 x)) = - sin (7 x) \cdot 7

= e^{4 x} \cdot 4 cos (7 x) + (- sin (7 x) \cdot 7) e^{4 x}

Simplify

= 4 e^{4 x} cos (7 x) - 7 e^{4 x} sin (7 x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^{4x}cos(7x) ?
The derivative of e^{4x}cos(7x) is 4e^{4x}cos(7x)-7e^{4x}sin(7x)
What is the first derivative of e^{4x}cos(7x) ?
The first derivative of e^{4x}cos(7x) is 4e^{4x}cos(7x)-7e^{4x}sin(7x)