Question

If y= lnx prove that dy/dx=1/x

Answer 1

by definition....

int(1/x) = lnx

Answer 2

y = ln x

e^y = x

now differentiate both sides with respect to x

Answer 3

use the definition of
f'(x)= lim h-->0 ([f(x+h)- f(h)/h)

Answer 4

so u have
f(x)=ln x

\( f'(x) = \lim_{h \rightarrow 0}\frac{f(x+h)-f(h)}{h}\)

Answer 5

\( f'(x)=\lim_{h \rightarrow 0}\frac{\ln (x+h)- \ln h} {h}\)

Answer 6

e^y = x

e^y dy/dx = 1