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Differentiation (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Differentiation (p-1)1 Mark
Question
If $x = y +\frac{1}{y}$ then $\frac{d y}{d x}=$
✓

Answer

$
\frac{y^2}{y^2-1}
$
Hint:
$
\begin{aligned}
& \quad \frac{d x}{d y}=\frac{d}{d y}\left(y+\frac{1}{y}\right)=1-\frac{1}{y^2}=\frac{y^2-1}{y^2} \\
& \therefore \frac{d y}{d x}=\frac{1}{\left(\frac{d x}{d y}\right)}=\frac{y^2}{y^2-1}
\end{aligned}
$

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