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Popular Calculus >

derivative of e^{6xsin(2x})

Solution

\frac{d}{d x} (e^{6 x s i n (2 x)})

Solution

e^{6 x s i n (2 x)} \cdot 6 (sin (2 x) + 2 x cos (2 x))

Solution steps

\frac{d}{d x} (e^{6 x s i n (2 x)})

Apply the chain rule:

e^{6 x s i n (2 x)} \frac{d}{d x} (6 x sin (2 x))

= e^{6 x s i n (2 x)} \frac{d}{d x} (6 x sin (2 x))

\frac{d}{d x} (6 x sin (2 x)) = 6 (sin (2 x) + 2 x cos (2 x))

= e^{6 x s i n (2 x)} \cdot 6 (sin (2 x) + 2 x cos (2 x))

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^{6xsin(2x}) ?
The derivative of e^{6xsin(2x}) is e^{6xsin(2x)}*6(sin(2x)+2xcos(2x))
What is the first derivative of e^{6xsin(2x}) ?
The first derivative of e^{6xsin(2x}) is e^{6xsin(2x)}*6(sin(2x)+2xcos(2x))