Is the function `f(x) = x^3`, an odd function or an even function?

The function f(x) = x has

If f(x) is an even function, state whether f'(x) is an odd function or an even function.

The function f (x) = 2-3 x is

On R, the function f(x) = 7x - 3 is

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?

The function f(x)=e^(|x|) is

If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x) , then f(x) is, (given f(0) = 0) a. an even function b. an odd function c. neither even nor odd function d. can't say

The function f(x)=x^(1/3)(x-1)