Solution assignment 24 Product and Quotient rule

Return to Assignments Product and Quotient rule

Assignment 24

Differentiate:

y=\displaystyle\frac{x+4}{x^2-16}, x\neq4 and x\neq{-4}

Solution

It is faster to simplify this function first. We can write by factorizing the denominator:

y=\displaystyle\frac{x+4}{(x+4)(x-4)}=\displaystyle\frac{1}{x-4}

We know:

f'(x)=0 and g'(x)=1

and thus the quotient rule yields:

y'=\displaystyle\frac{(x-4)\cdot0-1.1}{(x-4)^2}=-\displaystyle\frac{1}{(x-4)^2}

Note that both the original function and the simplified function are discontinuous for x=4 and x=-4 and cannot be differentiated in these points.

Return to Assignments Product and Quotient rule

0
Web Design BangladeshWeb Design BangladeshMymensingh