Solution assignment 03 Implicit differentiation

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Assignment 3

Calculate y' if:

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

Solution

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.

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