Question

Find `"dy"/"dx"`, if Differentiate 5^x with respect to log x

Answer 1

Let u = 5^x and v = log x

u = 5^x 

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)`