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

The answer to (\partial)/(\partial x)((zx-y)/(sqrt(x))) is (zx+y)/(2xsqrt(x))

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

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

\frac{z x + y}{2 x x}

Solution steps

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

Treat

z, y

as constants

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= \frac{z x + y}{2 x x}

\frac{d}{d x} (3^{x} - 1)

\int_{0}^{2} r^{3} d r

\int_{0}^{\infty} sin (7 x) d x

\int - \frac{3}{2} x^{2} + 3 x^{4} - 2 d x

\frac{d}{d x} (\frac{1}{2} sec (x) - \frac{1}{3} csc (x))

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