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Popular >

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

Solution

\frac{d}{d x} (e^{- x} \cdot 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

derivative of e^{1/(x^3})

\frac{d}{d x} (e^{\frac{1}{x ^{3}}})

(dy)/(dx)y=(y+1)(2x+1),y(-1)=1

\frac{d y}{d x} y = (y + 1) (2 x + 1), y (- 1) = 1

integral of z^2(z^3-1)^6

\int z^{2} (z^{3} - 1)^{6} d z

integral of p(p+6)^5

\int p (p + 6)^{5} d p

integral of 2/(1-4x^2)

\int \frac{2}{1 - 4 x ^{2}} d x

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)