What is (\partial)/(\partial y)(xz+e^{-x^2+y}) ?

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

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(\partial)/(\partial y)(xz+e^{-x^2+y})

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

e^{y - x^{2}}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x z) = 0

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

= 0 + e^{- x^{2} + y}

Simplify

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

k = 4 \sum \infty \frac{1}{( k + 3 ) ^{4}}

\int \frac{1}{4 x ^{2} + 4 x + 2} d x

e^{- t} cos (4 t) + \frac{t}{5}

x \to 2 lim (sin (x - 2))

\frac{\partial}{\partial x} (50 - x^{2} - y^{2})

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