Some results on differentiability

Every polynomial function is differentiable at each x Є R.

The exponential function is differentiable a^x, a>o is differentiable at each x Є R.

Every constant function is differentiable at each x Є R.

The logarithmic function is differentiable at each point in its domain.

The trigonometric and inverse-trigonometrics functions are differentiable at each point in their domains.

The sum, difference, product and quotient of two differentiable functions are differentiable.

The composition of differentiable function is a differential function.