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Question
If `y = sqrt(x) + 1/sqrt(x)`, then`(dy)/(dx)` at x = 1 is ______.
Options
1
`1/2`
`1/sqrt(2)`
0
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Solution
If `y = sqrt(x) + 1/sqrt(x)`, then`(dy)/(dx)` at x = 1 is 0.
Explanation:
Given that `y = sqrt(x) + 1/sqrt(x)`
`(dy)/(dx) = 1/(2sqrt(x)) - 1/(2x^(3/2))`
`((dy)/(dx))_("at" x = 1) = 1/2 - 1/2` = 0
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