What is (\partial)/(\partial x)(sqrt(xy-x)) ?

The answer to (\partial)/(\partial x)(sqrt(xy-x)) is (y-1)/(2sqrt(xy-x))

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(\partial)/(\partial x)(sqrt(xy-x))

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

\frac{y - 1}{2 x y - x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x y - x} (y - 1) : \frac{y - 1}{2 x y - x}

= \frac{y - 1}{2 x y - x}

x^{3} (x - 4)

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

(2, - 5), (- 8, 4)

\int x^{3} 14 + x^{4} d x

5 x e^{x}

What is (\partial)/(\partial x)(sqrt(xy-x)) ?
The answer to (\partial)/(\partial x)(sqrt(xy-x)) is (y-1)/(2sqrt(xy-x))