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Popular >

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

Solution

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

Solution

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

Simplify

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

Graph

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Frequently Asked Questions (FAQ)

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