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Popular >

derivative of 2ye^{-x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

Simplify

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

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\int 4 \frac{ln ( x )}{x} d x

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Frequently Asked Questions (FAQ)

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