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Question
`8^x/x^8`
Solution
Let y = `8^x/x^8`
Taking log on both sides, we get,
log y = `log 8^x/x^8`
⇒ log y = `log 8^x - log x^8`
⇒ log y = x log 8 – 8 log x
Differentiating both sides w.r.t. x
⇒ `1/y * "dy"/"dx" = log 8.1 - 8/x`
⇒ `"dy"/"dx" = y [log 8 - 8/x]`
Hence, `"dy"/"dx" = 8^x/x^8 [log 8 - 8/x]`
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