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

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

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

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

- e^{x - y}

Solution steps

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

Treat

x

as a constant

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) = - 1

= e^{x - y} (- 1)

Simplify

= - e^{x - y}

\frac{\partial}{\partial x} (- y lo g_{10} (x) - (1 - y) lo g_{10} (1 - x))

\int cos^{5} (x) d x

x \to 9 lim (cos (\frac{π x}{4}))

y \to \infty lim (\frac{2 y ^{2} - 3 y + 5}{y ^{2} - 5 y + 2})

x \to 2 lim (x^{3} + 3 x^{2})

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