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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int 10 x - 7 d x

\frac{d}{d x} ((x^{3} + 1)^{\frac{1}{2}})

(x - 2)^{2}

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

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