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Popular >

derivative of e^xsin(8x)

Solution

\frac{d}{d x} (e^{x} sin (8 x))

Solution

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

Solution steps

\frac{d}{d x} (e^{x} sin (8 x))

Apply the Product Rule:

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

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

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

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

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of e^xsin(8x) ?
The derivative of e^xsin(8x) is e^xsin(8x)+cos(8x)*8e^x
What is the first derivative of e^xsin(8x) ?
The first derivative of e^xsin(8x) is e^xsin(8x)+cos(8x)*8e^x