What is the derivative of e^{-2x}y ?

The derivative of e^{-2x}y is -2e^{-2x}y+e^{-2x}(dy)/(dx)

What is the first derivative of e^{-2x}y ?

The first derivative of e^{-2x}y is -2e^{-2x}y+e^{-2x}(dy)/(dx)

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

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

Solution steps

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

Apply the Product Rule:

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

f = e^{- 2 x}, g = y

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

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

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

Simplify

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

\frac{d}{d x} (sec^{2} (2 x) - tan^{2} (2 x))

\int \frac{28 x ^{2}}{4 - x ^{2}} d x

\int \frac{x ^{3}}{( x ^{2} + 4 x + 5 ) ^{2}} d x

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

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

What is the derivative of e^{-2x}y ?
The derivative of e^{-2x}y is -2e^{-2x}y+e^{-2x}(dy)/(dx)
What is the first derivative of e^{-2x}y ?
The first derivative of e^{-2x}y is -2e^{-2x}y+e^{-2x}(dy)/(dx)