What is (\partial)/(\partial y)(-3xe^{-xy}) ?

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

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(\partial)/(\partial y)(-3xe^{-xy})

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int e^{- 2 x} sin (e^{- x}) d x

\frac{d}{d t} (1 - t^{3})

\frac{\partial}{\partial y} (x arctan (yz))

\int e^{- (x^{2} + 1)} x d x

\frac{d}{d x} (x^{3} - 6 x^{2} + 9 x)

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