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

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

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(\partial)/(\partial y)(-e^{-xy})

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

e^{- x y} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= - \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

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

Simplify

= e^{- x y} x

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

\frac{d}{d x} (\frac{3 x}{( x ^{2} + 1 )})

f (x) = 7 x - x^{2}, at x = 1

(sin (2 t))^{^{'}}

\int_{0}^{π} 5 x^{2} sin (\frac{1}{2} x) d x

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