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Question
Differentiate the following w.r.t.x. :
y = `(x^2 + 3)/(x^2 - 5)`
Sum
Solution
Let y = `(x^2 + 3)/(x^2 - 5)`
∴ `("d"y)/("d"x) = "d"/("d"x) [(x^2 + 3)/(x^2 - 5)]`
= `((x^2 - 5) "d"/("d"x) (x^2 + 3) - (x^2 + 3) "d"/("d"x) (x^2 - 5))/(x^2 - 5)^2`
= `((x^2 - 5)(2x + 0) - (x^2 + 3)(2x - 0))/(x^2 - 5)^2`
= `(2x[(x^2 - 5) - (x^2 + 3)])/(x^2 - 5)^2`
= `(- 16x)/(x^2 - 5)^2`
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Derivative of Algebraic Functions
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Chapter 9: Differentiation - Exercise 9.2 [Page 192]
