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Popular >

derivative of e^xsin(2x)

Solution

derivative of

e^{x} sin (2 x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

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

Popular Examples

derivative of ln(x/k)

\frac{d}{d x} (ln (\frac{x}{k}))

integral from-a to a of 1/((s-x)^2)

\int_{- a}^{a} \frac{1}{( s - x ) ^{2}} d x

derivative of (x^2-4/(x^2-2x))

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} - 2 x})

integral of 2/(x^{2/3)}

\int \frac{2}{x ^{\frac{2}{3}}} d x

2y*(dy)/(dx)=x(y^2+1)

2 y \cdot \frac{d y}{d x} = x (y^{2} + 1)

Frequently Asked Questions (FAQ)

What is the derivative of e^xsin(2x) ?
The derivative of e^xsin(2x) is e^xsin(2x)+cos(2x)*2e^x
What is the first derivative of e^xsin(2x) ?
The first derivative of e^xsin(2x) is e^xsin(2x)+cos(2x)*2e^x