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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Simplify

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

\frac{d y}{d x}, y = x^{π}

t y^{^{'}} + t^{2} + t y - y = 0

h \to 0 lim (\frac{( 1 + h ) ^{9} - 1}{h})

\frac{d}{d x} (x^{3} + 6 x^{2})

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