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Popular >

derivative of e^{-x}cos(2x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = e^{- x}, g = cos (2 x)

= \frac{d}{d x} (e^{- x}) cos (2 x) + \frac{d}{d x} (cos (2 x)) e^{- x}

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

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

Simplify

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

Popular Examples

integral from 0 to 1 of x/(sqrt(1-x^2))

\int_{0}^{1} \frac{x}{1 - x ^{2}} d x

(xdy)/(dx)=5xe^x-y+6x^2

\frac{x d y}{d x} = 5 x e^{x} - y + 6 x^{2}

integral of (x^5-4x)^2(5x^4-4)

\int (x^{5} - 4 x)^{2} (5 x^{4} - 4) d x

limit as x approaches 0+of 1/(1+1/x)

x \to 0 + lim (\frac{1}{1 + \frac{1}{x}})

derivative of-8

\frac{d}{d x} (- 8)

Frequently Asked Questions (FAQ)

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