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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral from 0 to 2 of xsqrt(x^2+2)

\int_{0}^{2} x x^{2} + 2 d x

integral from 0 to 4 of (2x+5)

\int_{0}^{4} (2 x + 5) d x

derivative of x^2f(x)derivative of

x^{2} f (x)

integral of 1/(-\frac{1){x^2}+2x}-3

\int \frac{1}{- \frac{1}{x ^{2}} + 2 x} - 3 d x

inverse oflaplace 1/((s^2+4)^2*s)inverse laplace

\frac{1}{( s ^{2} + 4 ) ^{2} \cdot s}

Frequently Asked Questions (FAQ)

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