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Question
Find `"dy"/"dx"`, if Differentiate 5x with respect to log x
Solution
Let u = 5x and v = log x
u = 5x
Differentiating both sides w.r.t.x, we get
`"du"/"dx" = 5^"x" * log 5`
v = log x
Differentiating both sides w.r.t.x, we get
`"dv"/"dx" = 1/"x"`
∴ `"du"/"dv" = (("du"/"dx"))/(("dv"/"dx")) = (5^"x" log 5)/(1/"x") = "x"*5^"x" (log 5)`
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