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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

Popular Examples

limit as x approaches-1 of (|x|)/x

x \to - 1 lim (\frac{∣ x ∣}{x})

(dP)/(dt)=P(1/t-P)

\frac{d P}{d t} = P (\frac{1}{t} - P)

limit as x approaches 2 of x^2+x

x \to 2 lim (x^{2} + x)

(\partial)/(\partial v)(e^{{u}(v)}cos(v))

\frac{\partial}{\partial v} (e^{u (v)} cos (v))

derivative of y=e^{-12x}derivative of

y = e^{- 12 x}

Frequently Asked Questions (FAQ)

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