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

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

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

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

e^{x - y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x - y) = 1

= e^{x - y} \cdot 1

Simplify

= e^{x - y}

\int \frac{54}{1 - cos ( 6 x )} d x

\frac{d}{d x} (3 x^{2} - 2 x)

\frac{\partial}{\partial x} (x + y cos (y))

\int_{0}^{π} 2 x^{2} sin (\frac{1}{2} x) d x

\frac{4 x ^{2} + 2 x + 2}{x}

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