What is (\partial)/(\partial y)(xe^{y-1}) ?

The answer to (\partial)/(\partial y)(xe^{y-1}) is e^{y-1}x

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(\partial)/(\partial y)(xe^{y-1})

\frac{\partial}{\partial y} (x e^{y - 1})

e^{y - 1} x

Solution steps

\frac{\partial}{\partial y} (x e^{y - 1})

Treat

x

as a constant

Take the constant out:

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

= x \frac{\partial}{\partial y} (e^{y - 1})

Apply the chain rule:

e^{y - 1} \frac{\partial}{\partial y} (y - 1)

= e^{y - 1} \frac{\partial}{\partial y} (y - 1)

\frac{\partial}{\partial y} (y - 1) = 1

= x e^{y - 1} \cdot 1

Simplify

= e^{y - 1} x

\frac{d x}{d t} = 1.5 - \frac{2 x}{100 + t}

\int x (x - 6)^{2} d x

\int 2 e^{- \frac{x}{5}} d x

\frac{\partial}{\partial y} (\frac{y}{( x + 2 ) ^{2}})

\frac{d}{d x} (x (1 - x^{2})^{- \frac{1}{2}})

What is (\partial)/(\partial y)(xe^{y-1}) ?
The answer to (\partial)/(\partial y)(xe^{y-1}) is e^{y-1}x