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})

y = x^{3} - x, y = 0

x = - 2, x = 2, y = 8 x, y = x^{2} - 9

\frac{d}{d x} (lo g_{2} (x - 1))

x \to - 4 + lim (\frac{2}{x ^{2} - 16})

\int sin^{2} (x) cos^{3} (d) x 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))