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

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Question

(A) Given the equation $y = \frac{1}{a - z}$.To find $\frac{dz}{dy}$,we first differentiate $y$ with respect to $z$ using the chain rule or power rule

Vedclass · Accepted Answer

$(z - a)^2$

Vedclass · Answer

(A) Given the equation $y = \frac{1}{a - z}$.To find $\frac{dz}{dy}$,we first differentiate $y$ with respect to $z$ using the chain rule or power rule.$y = (a - z)^{-1}$.Applying the derivative with respect to $z$:$\frac{dy}{dz} = -1 \cdot (a - z)^{-2} \cdot \frac{d}{dz}(a - z)$.$\frac{dy}{dz} = -1 \cdot (a - z)^{-2} \cdot (-1) = (a - z)^{-2} = \frac{1}{(a - z)^2}$.Since $\frac{dz}{dy} = \frac{1}{\frac{dy}{dz}}$,we have:$\frac{dz}{dy} = (a - z)^2$.Since $(a - z)^2 = (z - a)^2$,the final result is $\frac{dz}{dy} = (z - a)^2$.

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

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