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Popular >

derivative of f(x)=e^{-x}sin(x)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

Popular Examples

integral of 2x-1/(e^{x^2)}

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

derivative of 14(4e^{x^2}x^3+6e^{x^2}x)derivative of

14 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

derivative of (x+7)*ln(x)derivative of

(x + 7) \cdot ln (x)

derivative of 1/(ln(x))derivative of

\frac{1}{ln ( x )}

limit as x approaches 3 of sqrt(4-x^2)

x \to 3 lim (4 - x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^{-x}sin(x) ?
The derivative of f(x)=e^{-x}sin(x) is -e^{-x}sin(x)+e^{-x}cos(x)
What is the first derivative of f(x)=e^{-x}sin(x) ?
The first derivative of f(x)=e^{-x}sin(x) is -e^{-x}sin(x)+e^{-x}cos(x)