Solution assignment 03 Implicit differentiation

Calculate $y'$ if:

$\displaystyle\frac{x}{y+1}=2$

Here it is not necessary to use implicit differentiation. We rewrite the expression:

$\displaystyle\frac{y+1}{x}=\displaystyle\frac{1}{2}$

or:

$y=\displaystyle\frac{1}{2}x-1$

thus:

$y'=\displaystyle\frac{1}{2}$

Applying the quotient rule would give the same result:

$\displaystyle\frac{(y+1).1-xy'}{(y+1)^2}=0$

thus:

$y'=\displaystyle\frac{y+1}{x}=\displaystyle\frac{1}{2}$

For the latter calculation we used the original expression.