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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

tangent of y=3+4x+7xe^x tangent of

y = 3 + 4 x + 7 x e^{x}

x^2y^{''}+3xy^'-35y=0

x^{2} y^{^{''}} + 3 x y^{^{'}} - 35 y = 0

integral of tan(x)(4cos(x)+8sec(x))

\int tan (x) (4 cos (x) + 8 sec (x)) d x

integral of (8x)/(1+x^2)

\int \frac{8 x}{1 + x ^{2}} d x

(dy)/(dx)+y^5x+6y=0

\frac{d y}{d x} + y^{5} x + 6 y = 0

Frequently Asked Questions (FAQ)

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