What is the derivative of e^{-xy} ?

The derivative of e^{-xy} is e^{-xy}(-y-x(dy)/(dx))

What is the first derivative of e^{-xy} ?

The first derivative of e^{-xy} is e^{-xy}(-y-x(dy)/(dx))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

ln (4 + x)

x \to 0 lim (x (e^{\frac{1}{x}} - 1))

\frac{d}{d x} (e^{2 s i n (x)})

5 x^{2} y^{^{'}} = y^{^{'}} + 9 x e^{- y}

\int ln (x) x^{7} d x

What is the derivative of e^{-xy} ?
The derivative of e^{-xy} is e^{-xy}(-y-x(dy)/(dx))
What is the first derivative of e^{-xy} ?
The first derivative of e^{-xy} is e^{-xy}(-y-x(dy)/(dx))