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})

Take the constant out:

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

= - \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})

\int_{1}^{\infty} (e^{- x}) d x

\int \frac{6}{x - 1} d x

\int 3 x + 2 d x

\frac{( x ^{2} + 3 ) d y}{d x} = x y, y (1) = 8

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))