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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x) = - 1

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

Simplify

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

\frac{\partial}{\partial x} ((A x^{c} + B y^{c})^{\frac{1}{c}})

\frac{\partial}{\partial x} (\frac{18}{x y})

\int_{1}^{6} k x d x

x \to - 2 lim (\frac{x ^{2} - 5}{2 - x})

\frac{d}{d x} (- 2 x - 2)

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