What is (\partial)/(\partial x)(x^3e^{-2y}) ?

The answer to (\partial)/(\partial x)(x^3e^{-2y}) is 3e^{-2y}x^2

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(\partial)/(\partial x)(x^3e^{-2y})

\frac{\partial}{\partial x} (x^{3} e^{- 2 y})

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

Solution steps

\frac{\partial}{\partial x} (x^{3} e^{- 2 y})

Treat

y

as a constant

Take the constant out:

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

= e^{- 2 y} \frac{\partial}{\partial x} (x^{3})

Apply the Power Rule:

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

= e^{- 2 y} \cdot 3 x^{3 - 1}

Simplify

= 3 e^{- 2 y} x^{2}

What is (\partial)/(\partial x)(x^3e^{-2y}) ?
The answer to (\partial)/(\partial x)(x^3e^{-2y}) is 3e^{-2y}x^2