DifferentiationHard
Question
Let ef(x) = ln x. If g(x) is the inverse function of f(x), then g′(x) equals to:
Options
A.ex
B.ex + x
C.ex + ex
D.ex + ln x
Solution
ef(x) = ln x
∵ f-1 (x) = g(x)
x = eef(x)
⇒ g(x) = f-1(x) = eex
⇒ g′(x) = eex .ex = eex + x
∵ f-1 (x) = g(x)
x = eef(x)
⇒ g(x) = f-1(x) = eex
⇒ g′(x) = eex .ex = eex + x
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