Question

find the derivative of ln x a​

Answer 1

Answer:

We begin with the inverse definition. If

y = ln x

then

ey = x

Now implicitly take the derivative of both sides with respect to x remembering to multiply by dy/dx on the left hand side since it is given in terms of y not x.

ey dy/dx = 1

From the inverse definition, we can substitute x in for ey to get

x dy/dx = 1

Finally, divide by x to get

dy/dx = 1/x

We have proven the following theorem