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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral of 19sin^2(xco)s^2x

\int 19 sin^{2} (x co) s^{2} x d x

integral of (2e^{-1/x})/(x^2)

\int \frac{2 e ^{- \frac{1}{x}}}{x ^{2}} d x

limit as x approaches infinity of 2+3-2

x \to \infty lim (2 + 3 - 2)

limit as x approaches 0 of (cos(x)-cos(x))/(x^2)

x \to 0 lim (\frac{cos ( x ) - cos ( x )}{x ^{2}})

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

Frequently Asked Questions (FAQ)

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