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

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

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

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

2 e^{- 2 x} y

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

= 2 e^{- 2 x} y

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25 y^{^{''}} + 10 y = 0

\frac{d}{d x} (- ln (4 x))

\int (- 8 sec (x) tan (x) - 3 sec^{2} (x)) d x

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