What is the derivative of x/z ?

The derivative of x/z is (z-x\frac{dz)/(dx)}{z^2}

What is the first derivative of x/z ?

The first derivative of x/z is (z-x\frac{dz)/(dx)}{z^2}

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\frac{d}{d x} (\frac{x}{z ( x )})

\frac{z - x \frac{d z}{d x}}{z ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{z})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} z - \frac{d z}{d x} x}{z ^{2}}

\frac{d x}{d x} = 1

= \frac{1 \cdot z - \frac{d z}{d x} x}{z ^{2}}

Simplify

= \frac{z - x \frac{d z}{d x}}{z ^{2}}

What is the derivative of x/z ?
The derivative of x/z is (z-x\frac{dz)/(dx)}{z^2}
What is the first derivative of x/z ?
The first derivative of x/z is (z-x\frac{dz)/(dx)}{z^2}