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Question
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
Solution
Let y = `(x^2 +"a"^2)/(x^2 - "a"^2)`
Differentiating w.r.t. x, we get
`dy/dx = d/dx((x^2 + "a"^2)/(x^2 - "a"^2))`
= `((x^2 - "a"^2)d/dx(x^2 + "a"^2) - (x^2 + "a"^2)d/dx(x^2 - "a"^2))/(x^2 - "a"^2)^2`
= `((x^2 - "a"^2)(d/dxx^2 + d/dx "a"^2)-(x^2 + "a"^2)(d/dxx^2 - d/dx "a"^2))/((x^2 - "a"^2)^2)`
= `((x^2 - "a"^2)(2x + 0) - (x^2 + "a"^2)(2x - 0))/((x^2 - "a"^2)^2)`
=`(2x(x^2 - "a"^2) - 2x(x^2 + "a"^2))/((x^2 - "a"^2)^2)`
= `(2x(x^2 - "a"^2 - x^2 - "a"^2))/((x^2 - "a"^2)^2)`
= `(2x(-2"a"^2))/((x^2 - "a"^2)^2)`
=`(-4x"a"^2)/((x^2 - "a"^2)^2)`
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