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Popular >

derivative of sin(12xe^{7x})

Solution

\frac{d}{d x} (sin (12 x) e^{7 x})

Solution

cos (12 x) \cdot 12 e^{7 x} + e^{7 x} \cdot 7 sin (12 x)

Solution steps

\frac{d}{d x} (sin (12 x) e^{7 x})

Apply the Product Rule:

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

f = sin (12 x), g = e^{7 x}

= \frac{d}{d x} (sin (12 x)) e^{7 x} + \frac{d}{d x} (e^{7 x}) sin (12 x)

\frac{d}{d x} (sin (12 x)) = cos (12 x) \cdot 12

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

= cos (12 x) \cdot 12 e^{7 x} + e^{7 x} \cdot 7 sin (12 x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sin(12xe^{7x}) ?
The derivative of sin(12xe^{7x}) is cos(12x)*12e^{7x}+e^{7x}*7sin(12x)
What is the first derivative of sin(12xe^{7x}) ?
The first derivative of sin(12xe^{7x}) is cos(12x)*12e^{7x}+e^{7x}*7sin(12x)