What is (\partial)/(\partial x)(sqrt(x(y-1))) ?

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

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(\partial)/(\partial x)(sqrt(x(y-1)))

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

\frac{y - 1}{2 x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x^{2} lo g_{2} (x))

(x^{3} - 25 x)^{12} (- 5)

\frac{d}{d t} (\frac{( 2 t + 1 ) ^{\frac{3}{2}}}{3})

f (x) = (3 x + 1) (6 x - 2)

\frac{1}{s \cdot ( s ^{2} + 5 s + 4 )}

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