Question

Hi

would you please show how to know if the function is differentiable or not ?
please show me the answer with examples

Answer 1

pretty broad question. Some examples:

All polynomials are differentiable.
Rational functions are differentiable except where their denominator is zero
All exponental functions are differentiable, as long as their epxonents are.
Same for logs, where domain > 0
Things with cusps, like absolute values, or fractional exponents, generally are not differentiable at their cusp.

In general, if the function is continuous and "smooth" in the sense that there are no pointy bits, where the slope changes abruptly, it us differentiable.

I think some time doing web searches and reviewing your textbook will provide many interesting examples.