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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{900}{( 2 q - 5 ) ^{2}} d q

\frac{d}{d x} (\frac{5}{3} x^{2})

x \to 0 lim (x \cdot sin (x))

\int_{1}^{\infty} 15 e^{- 5 x} d x

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

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