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Popular >

derivative of e^xcos(3x)

Solution

\frac{d}{d x} (e^{x} cos (3 x))

Solution

e^{x} cos (3 x) - 3 e^{x} sin (3 x)

Solution steps

\frac{d}{d x} (e^{x} cos (3 x))

Apply the Product Rule:

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

f = e^{x}, g = cos (3 x)

= \frac{d}{d x} (e^{x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{x}

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= e^{x} cos (3 x) + (- sin (3 x) \cdot 3) e^{x}

Simplify

= e^{x} cos (3 x) - 3 e^{x} sin (3 x)

Graph

Popular Examples

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x \to 5 - lim (\frac{x - 6}{x - 5})

maclaurin e^{-5x}maclaurin

e^{- 5 x}

3 y^{^{'}} - 6 y = 12

integral of cos^4(3x)sin(3x)

\int cos^{4} (3 x) sin (3 x) d x

t(d^2y)/(dt^2)+4(dy)/(dt)=t^2

t \frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} = t^{2}

Frequently Asked Questions (FAQ)

What is the derivative of e^xcos(3x) ?
The derivative of e^xcos(3x) is e^xcos(3x)-3e^xsin(3x)
What is the first derivative of e^xcos(3x) ?
The first derivative of e^xcos(3x) is e^xcos(3x)-3e^xsin(3x)