Question

y= 1/a-z, find dz/dy

Answer 1

given, y=1/a-z.
dy/dz=[d/dz(1)(a-z)-d/dz(a-z)(1)]/(a-z)²
=>dy/dz=[0-0+dy/dz]/(a-z)²
=>dy/dz=dz/dy/(a-z)²
=>dz/dy=(a-z)²×dy/dz.

Answer 2

$\frac{d z}{d y}=\frac{1}{y^{2}}$

Given:

Given in question is the equation as $y=\frac{1}{a-z }$, and to find out $\frac{d z}{d y}$.  

Solution:  

We need to differentiate the value of z with respect to y. Rearranging the given equation we get the equation in terms of  z  

$\begin{array}{l}{y=\frac{1}{a-z}} \\ {a-z=\frac{1}{y}} \\ {z=a-\left(\frac{1}{y}\right)} \\ {z=a-y^{-1}}\end{array}$

Differentiate z with respect to y  

$\begin{array}{l}{\frac{d z}{d y}=-(-1) y-1-1} \\ {\frac{d z}{d y}=y-2} \\ {\frac{d z}{d y}=\frac{1}{y^{2}}}\end{array}$