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

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

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

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

2 e^{- y} x

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

= e^{- y} (2 x - 0)

Simplify

= 2 e^{- y} x

\frac{\partial}{\partial x} (e^{(x - 1)^{2}} cos (y))

x \to 0 + lim (\frac{7}{x ^{3} - 2 x ^{2}})

\frac{d}{d t} ((t + 1) i + (sin (x^{2} + 4 x + 6)) j)

e^{3 t + 1}

\int (\frac{( x - 3 ) ^{3}}{x}) d x

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