MCQ
Sum
Choose the correct alternative.
If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?`
Options
`(2 - "x")/"x"`
`("x" - 2)/"x"`
`("e - x")/"ex"`
`("x - e")/"ex"`
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Solution
`("x" - 2)/"x"`
Explanation:
y = log `("e"^"x"/"x"^2)`
= log (ex) - log (x2)
= x log e - 2 log x
= x(1) - 2 log x
∴ y = x - 2 log x
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = 1 - 2(1/"x") = ("x - 2")/"x"`
Concept: Derivative - Derivatives of Logarithmic Functions
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