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Popular >

derivative of (e^{3x}(cos(2x)))

Solution

\frac{d}{d x} ((e^{3 x}) (cos (2 x)))

Solution

3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x)

Solution steps

\frac{d}{d x} ((e^{3 x}) (cos (2 x)))

Apply the Product Rule:

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

f = e^{3 x}, g = cos (2 x)

= \frac{d}{d x} (e^{3 x}) cos (2 x) + \frac{d}{d x} (cos (2 x)) e^{3 x}

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= e^{3 x} \cdot 3 cos (2 x) + (- sin (2 x) \cdot 2) e^{3 x}

Simplify

= 3 e^{3 x} cos (2 x) - 2 e^{3 x} sin (2 x)

Popular Examples

16 y^{''} + 8 y^{'} + y = 0

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x \to 0 lim (\frac{tan ( 4 x ) cos ( 6 x ) - tan ( 4 x )}{24 x ^{3}})

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x \to + 1 lim (\frac{x - 1}{x ^{6} - 1})

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(\partial)/(\partial x)(3(y-1)^3(x-6))

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Frequently Asked Questions (FAQ)

What is the derivative of (e^{3x}(cos(2x))) ?
The derivative of (e^{3x}(cos(2x))) is 3e^{3x}cos(2x)-2e^{3x}sin(2x)
What is the first derivative of (e^{3x}(cos(2x))) ?
The first derivative of (e^{3x}(cos(2x))) is 3e^{3x}cos(2x)-2e^{3x}sin(2x)