If y = frac{1}{a - z},then frac{dz}{dy} = | vedclass

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Question

(A) Given the equation $y = \frac{1}{a - z}$.Rearranging the equation to solve for $z$:$a - z = \frac{1}{y}$$z = a - \frac{1}{y}$Now,differentiate $z$

Vedclass · Accepted Answer

$(z - a)^2$

Vedclass · Answer

(A) Given the equation $y = \frac{1}{a - z}$.Rearranging the equation to solve for $z$:$a - z = \frac{1}{y}$$z = a - \frac{1}{y}$Now,differentiate $z$ with respect to $y$:$\frac{dz}{dy} = \frac{d}{dy}(a - \frac{1}{y})$Since the derivative of a constant $a$ is $0$ and the derivative of $-\frac{1}{y}$ is $\frac{1}{y^2}$:$\frac{dz}{dy} = 0 - (-1) 	imes y^{-2} = \frac{1}{y^2}$Substitute $y = \frac{1}{a - z}$ back into the expression:$\frac{dz}{dy} = \frac{1}{(\frac{1}{a - z})^2} = (a - z)^2$Since $(a - z)^2 = (z - a)^2$,the final result is $(z - a)^2$.

If $y = \frac{1}{a - z}$,then $\frac{dz}{dy} = $

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