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Question
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
Options
`1/(x + 4)`
`sqrt(x)/((sqrt(x + 2))^2`
`1/(2sqrt(x))`
`x/((sqrt(x) + 2)^2`
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Solution
`1/(2sqrt(x))`
Explanation:
y = `(x - 4)/(sqrtx + 2)`
= `((sqrt(x))^2 - (2)^2)/(sqrt(x) + 2)`
= `((sqrt(x) + 2) (sqrt(x) - 2))/((sqrt(x) + 2)`
∴ y = `sqrt(x) - 2`
Differentiating w.r.t.x, we get
`("d"y)/("d"x) = 1/(2sqrt(x))`
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