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Popular >

d/(d{x)}({x}{z}+e^{-{x}^2+{y}})

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

What is the d/(d{x)}({x}{z}+e^{-{x}^2+{y}}) ?
The d/(d{x)}({x}{z}+e^{-{x}^2+{y}}) is {z}+e^{-{x}^2+{y}}(-2{x}+d/(d{x)}({y}))
What is the first d/(d{x)}({x}{z}+e^{-{x}^2+{y}}) ?
The first d/(d{x)}({x}{z}+e^{-{x}^2+{y}}) is {z}+e^{-{x}^2+{y}}(-2{x}+d/(d{x)}({y}))