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Question
Differentiate the following w.r.t.x. :
y = `(sqrt(x) + 5)/(sqrt(x) - 5)`
Sum
Solution
y = `(sqrt(x) + 5)/(sqrt(x) - 5)`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x) ((sqrt(x) + 5)/(sqrt(x) - 5))`
= `((sqrt(x) - 5) "d"/("d"x) (sqrt(x) + 5) - (sqrt(x) + 5) "d"/("d"x) (sqrt(x) - 5))/(sqrt(x) - 5)^2`
= `((sqrt(x) - 5) (1/(2sqrt(x))) - (sqrt(x) + 5)(1/(2sqrt(x))))/(sqrt(x) - 5)^2`
= `(1/(2sqrt(x)) (sqrt(x) - 5 - sqrt(x) - 5))/(sqrt(x) - 5)^2`
= `(1/(2sqrt(x)) (-10))/(sqrt(x) - 5)^2`
= `(-5)/(sqrt(x) (sqrt(x) - 5)^2`
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Derivative of Algebraic Functions
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