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Question
Differentiate the following:
y = `5^((-1)/x)`
Solution
y = `5^((-1)/x)`
y = `"e"log^(5 - 1/x)`
y = `"e"^(- 1/xlog 5)`
`("d"y)/("d"x) = "e"^(- 1/x log 5) xx "d"/("d"x) (- 1/x log 5)`
= `"e"^(- 1/x log 5) xx - log 5((-1) x^(- 1 - 1))`
= `"e"^(- 1/x log 5) xx (log 5) x^(- 2)`
= `"e"^(log 5 - 1/x) ((log 5))/x^2`
`("d"y)/("d"x) = (5^(-1/x) (log 5))/x^2`
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