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Popular >

derivative of e^xsin(3x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

derivative of 1500x+3000(2x+3)^{-1}-1000 derivative of

1500 x + 3000 (2 x + 3)^{- 1} - 1000

integral of-ln(x)-(ln(x))/(16)

\int - ln (x) - \frac{ln ( x )}{16} d x

inverse oflaplace 2/(s^2)+(24)/s+1/8 inverse laplace

\frac{2}{s ^{2}} + \frac{24}{s} + \frac{1}{8}

derivative of (500/x)

\frac{d}{d x} (\frac{500}{x})

limit as x approaches 1 of 1/(x^2+1)

x \to 1 lim (\frac{1}{x ^{2} + 1})

Frequently Asked Questions (FAQ)

What is the derivative of e^xsin(3x) ?
The derivative of e^xsin(3x) is e^xsin(3x)+cos(3x)*3e^x
What is the first derivative of e^xsin(3x) ?
The first derivative of e^xsin(3x) is e^xsin(3x)+cos(3x)*3e^x