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Popular >

derivative of f(x)=e^{3x}sin(3x)

Solution

derivative of

f (x) = e^{3 x} sin (3 x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Graph

Popular Examples

derivative of 15e^{-4x}-60xe^{-4x}

\frac{d}{d x} (15 e^{- 4 x} - 60 x e^{- 4 x})

y^{''}+y^'-2y=x^2

y^{^{''}} + y^{^{'}} - 2 y = x^{2}

derivative of f(x)= 9/(\sqrt[5]{x)}derivative of

f (x) = \frac{9}{5 x}

integral of (x-7)^3

\int (x - 7)^{3} d x

derivative of 2/(2x+e^{2x})

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

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^{3x}sin(3x) ?
The derivative of f(x)=e^{3x}sin(3x) is e^{3x}*3sin(3x)+cos(3x)*3e^{3x}
What is the first derivative of f(x)=e^{3x}sin(3x) ?
The first derivative of f(x)=e^{3x}sin(3x) is e^{3x}*3sin(3x)+cos(3x)*3e^{3x}