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Popular >

derivative of f(x)=e^xsin^2(x)

Solution

derivative of

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

Solution

e^{x} sin^{2} (x) + sin (2 x) 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)) = sin (2 x)

= e^{x} sin^{2} (x) + sin (2 x) e^{x}

Popular Examples

integral from 0 to t of te^{-t}

\int_{0}^{t} t e^{- t} d t

(\partial)/(\partial x)(e^{x-2})

\frac{\partial}{\partial x} (e^{x - 2})

derivative of 8x^3+4x^2-5x+4

\frac{d}{d x} (8 x^{3} + 4 x^{2} - 5 x + 4)

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arcsin (5 x)

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\frac{( 8 x ) ^{9}}{9}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^xsin^2(x) ?
The derivative of f(x)=e^xsin^2(x) is e^xsin^2(x)+sin(2x)e^x
What is the first derivative of f(x)=e^xsin^2(x) ?
The first derivative of f(x)=e^xsin^2(x) is e^xsin^2(x)+sin(2x)e^x