What is (\partial)/(\partial y)(xe^{y-z^2}) ?

The answer to (\partial)/(\partial y)(xe^{y-z^2}) is e^{y-z^2}x

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(\partial)/(\partial y)(xe^{y-z^2})

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

e^{y - z^{2}} x

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

e^{y - z^{2}} \frac{\partial}{\partial y} (y - z^{2})

= e^{y - z^{2}} \frac{\partial}{\partial y} (y - z^{2})

\frac{\partial}{\partial y} (y - z^{2}) = 1

= x e^{y - z^{2}} \cdot 1

Simplify

= e^{y - z^{2}} x

\frac{d}{d x} (ln (2 + e^{x}))

\int_{- 1}^{1} \frac{2 x}{( x + 7 ) ^{2}} d x

\frac{\partial}{\partial z} (2 x yz)

6 x^{2} y^{^{'}} = y^{^{'}} + 3 x e^{- y}

\frac{d}{d x} (- \frac{1}{2} + \frac{7}{5} x^{3})

What is (\partial)/(\partial y)(xe^{y-z^2}) ?
The answer to (\partial)/(\partial y)(xe^{y-z^2}) is e^{y-z^2}x