How do you find the derivative of x/(x^2-4)xx24?

2 Answers

The answer is in the explanation section.

Explanation:

y = x/(x^2 - 4)y=xx24

dy/dxdydx = (((x^2 - 4) (1)) -((x) (2x)))/(x^2 - 4)^2((x24)(1))((x)(2x))(x24)2 [by Quotient Rule]

dy/dxdydx = ((x^2- 4) - (2x^2))/(x^2 - 4)^2(x24)(2x2)(x24)2

dy/dxdydx = (x^2- 4 - 2x^2)/(x^2 - 4)^2x242x2(x24)2

dy/dxdydx = (-x^2- 4 )/(x^2 - 4)^2x24(x24)2

Aug 11, 2015

Use the product, power and chain rules to find:

d/(dx) (x/(x^2-4)) = -(x^2+4)/(x^2-4)^2ddx(xx24)=x2+4(x24)2

Explanation:

d/(dx) (x/(x^2-4)) = d/(dx) x(x^2-4)^-1ddx(xx24)=ddxx(x24)1

=(d/(dx) x)(x^2-4)^-1 + x(d/(dx) (x^2-4)^-1)=(ddxx)(x24)1+x(ddx(x24)1) [Product Rule]

=(x^2-4)^-1 - 2x^2(x^2-4)^-2=(x24)12x2(x24)2 [Power Rule and Chain Rule]

=((x^2-4)-2x^2)/(x^2-4)^2=(x24)2x2(x24)2

=-(x^2+4)/(x^2-4)^2=x2+4(x24)2