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Popular >

derivative of e^xcos(6x)

Solution

\frac{d}{d x} (e^{x} cos (6 x))

Solution

e^{x} cos (6 x) - 6 e^{x} sin (6 x)

Solution steps

\frac{d}{d x} (e^{x} cos (6 x))

Apply the Product Rule:

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

f = e^{x}, g = cos (6 x)

= \frac{d}{d x} (e^{x}) cos (6 x) + \frac{d}{d x} (cos (6 x)) e^{x}

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

\frac{d}{d x} (cos (6 x)) = - sin (6 x) \cdot 6

= e^{x} cos (6 x) + (- sin (6 x) \cdot 6) e^{x}

Simplify

= e^{x} cos (6 x) - 6 e^{x} sin (6 x)

Graph

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\int_{- 1}^{3} (x^{3} + 5 x) d x

limit as y approaches infinity of e^y

y \to \infty lim (e^{y})

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\int 2 x x^{2} + 2 d x

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\int 8 tan^{4} (x) sec^{6} (x) d x

derivative of-e/x derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of e^xcos(6x) ?
The derivative of e^xcos(6x) is e^xcos(6x)-6e^xsin(6x)
What is the first derivative of e^xcos(6x) ?
The first derivative of e^xcos(6x) is e^xcos(6x)-6e^xsin(6x)