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

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

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

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

- e^{- x} (x - y^{2}) + e^{- x}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x}, g = x - y^{2}

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

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

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

= (- e^{- x}) (x - y^{2}) + 1 \cdot e^{- x}

Simplify

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

\frac{d}{d x} (arcsech (1 - x^{2}))

\frac{d}{d x} (x \cdot e^{x y})

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

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

\frac{d}{d x} (\frac{x - 6}{7 x ^{2} e ^{x}})

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