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Popular >

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

Solution

derivative of

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)

Popular Examples

limit as x approaches infinity of (4x+1)/(12x^2-7)

x \to \infty lim (\frac{4 x + 1}{12 x ^{2} - 7})

integral of 1/(y+3)

\int \frac{1}{y + 3} d y

taylor sin(x),0.5 taylor

sin (x), 0.5

(3x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=6

(3 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0, y (1) = 6

(dy)/(dt)=csc(y)

\frac{d y}{d t} = csc (y)

Frequently Asked Questions (FAQ)

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