What is the d/(dy)(-e^{-xy}) ?

The d/(dy)(-e^{-xy}) is e^{-xy}x

What is the first d/(dy)(-e^{-xy}) ?

The first d/(dy)(-e^{-xy}) is e^{-xy}x

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

e^{- x y} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= e^{- x y} x

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