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Popular >

derivative of e^{5x}cos(8x)

Solution

derivative of

e^{5 x} cos (8 x)

Solution

5 e^{5 x} cos (8 x) - 8 e^{5 x} sin (8 x)

Solution steps

\frac{d}{d x} (e^{5 x} cos (8 x))

Apply the Product Rule:

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

f = e^{5 x}, g = cos (8 x)

= \frac{d}{d x} (e^{5 x}) cos (8 x) + \frac{d}{d x} (cos (8 x)) e^{5 x}

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

\frac{d}{d x} (cos (8 x)) = - sin (8 x) \cdot 8

= e^{5 x} \cdot 5 cos (8 x) + (- sin (8 x) \cdot 8) e^{5 x}

Simplify

= 5 e^{5 x} cos (8 x) - 8 e^{5 x} sin (8 x)

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Frequently Asked Questions (FAQ)

What is the derivative of e^{5x}cos(8x) ?
The derivative of e^{5x}cos(8x) is 5e^{5x}cos(8x)-8e^{5x}sin(8x)
What is the first derivative of e^{5x}cos(8x) ?
The first derivative of e^{5x}cos(8x) is 5e^{5x}cos(8x)-8e^{5x}sin(8x)