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

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

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

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

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

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (4^{x} + 1)

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

x \to 2 lim (\frac{4}{( x - 2 ) ^{3}})

\frac{d}{d x} (d cos (x) + x^{2} sin (x))

n = 1 \sum \infty \frac{3}{n ^{\frac{5}{3}}}

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