What is (\partial)/(\partial x)(e^{x+x*y-2*y}) ?

The answer to (\partial)/(\partial x)(e^{x+x*y-2*y}) is e^{x+xy-2y}(y+1)

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(\partial)/(\partial x)(e^{x+xy-2y})

\frac{\partial}{\partial x} (e^{x + x \cdot y - 2 \cdot y})

e^{x + x y - 2 y} (y + 1)

Solution steps

\frac{\partial}{\partial x} (e^{x + x y - 2 y})

Treat

y

as a constant

Apply the chain rule:

e^{x + x y - 2 y} \frac{\partial}{\partial x} (x + x y - 2 y)

= e^{x + x y - 2 y} \frac{\partial}{\partial x} (x + x y - 2 y)

\frac{\partial}{\partial x} (x + x y - 2 y) = y + 1

= e^{x + x y - 2 y} (y + 1)

\int_{1}^{\infty} x e^{- 6 x} d x

\frac{\partial}{\partial x} (3 x^{2} + 12 x + 2 x y + 8 y)

\frac{d}{d x} (\frac{4 x - 7}{x - 2})

\int e^{4 x - 2} d x

x + \frac{6}{x}

What is (\partial)/(\partial x)(e^{x+x*y-2*y}) ?
The answer to (\partial)/(\partial x)(e^{x+x*y-2*y}) is e^{x+xy-2y}(y+1)