Which of the following functions are not derivable at `x=0?`

Which of the following functions is differentiable at x = 0?

Left hand derivative and right hand derivative of a function f(x) at a point x=a are defined as f'(a^-)=lim_(hrarr0^(+))(f(a)-f(a-h))/(h) =lim_(hrarr0^(+))(f(a+h)-f(a))/(h) andf'(a^(+))=lim_(hrarr0^(+))(f(a+h)-f(a))/(h) =lim_(hrarr0^(+))(f(a)-f(a+h))/(h) =lim_(hrarr0^(+)) (f(a)-f(x))/(a-x) respectively. Let f be a twice differentiable function. We also know that derivative of a even function is odd function and derivative of an odd function is even function. If f is even function, which of the following is right hand derivative of f' at x=a?

Find derivative of each of the following functions: e^x + log x

Find the maximum and the minimum values, if any, of the following functions, without using the derivative: x + 1/x , x > 0

For the following function , evaluate the derivative at the indicated value (s) : f(x) =x , x=1.

For the following function , evaluate the derivative at the indicated value (s) : f(x) =99x ,x = 100.

For the following function , evaluate the derivative at the indicated value (s) : f(x) =x^2-2, x=10 .

Examine the derivability of the following functions at the specified points: |x|at x=0

Examine the derivability of the following functions at the specified points: |x|^2 at x=0