What is the derivative of ye^{-x} ?

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

What is the first derivative of ye^{-x} ?

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

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

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

Solution steps

\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}

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

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

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

Simplify

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

\frac{d P}{d t} = a P - b P^{2}

x \to 2 lim (\frac{( x + 3 )}{x - 2})

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

cos (x), 0.5, 0 \leq x \leq π

\int (2 x - 3) tan (7 x^{2} - 21 x + 9) d x

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