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Popular >

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

Solution

derivative of

e^{2 x} 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

xy^{''}=y^'+(y^')^2

x y^{^{''}} = y^{^{'}} + (y^{^{'}})^{2}

integral of (9+x)/(x^2)

\int \frac{9 + x}{x ^{2}} d x

tangent of f(x)=-3-7x^2,\at x=42 tangent of

f (x) = - 3 - 7 x^{2}, at x = 42

derivative of e^{-0.05x}

\frac{d}{d x} (e^{- 0.05 x})

tangent of f(x)= 1/x+4,\at x=-4 tangent of

f (x) = \frac{1}{x} + 4, at x = - 4

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}