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Popular >

derivative of e^{2x}*sin(3x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

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

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

Popular Examples

taylor 1/(e^{1/x+1)-1}taylor

\frac{1}{e ^{\frac{1}{x} + 1} - 1}

integral of 1/(x^2sqrt(9-x^2))

\int \frac{1}{x ^{2} 9 - x ^{2}} d x

derivative of (-x^2-6)/((x^2-6)^2)derivative of

\frac{- x ^{2} - 6}{( x ^{2} - 6 ) ^{2}}

tangent of (5x)/(x+4)(1.1)tangent of

\frac{5 x}{x + 4} (1.1)

y^{''}+5y^'=e^{-t}

y^{^{''}} + 5 y^{^{'}} = e^{- t}

Frequently Asked Questions (FAQ)

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