Suppose that the function 0, \infty) \rightarrow R" alt="f0, \infty) \rightarrow R" /> is differentiable and let c>0. Now define 0, \infty) \rightarrow R " alt="g0, \infty) \rightarrow R " /> by for x>0. Just using the definition of derivative, show that for x>0

My work:

according to the defnition of derivative, g(x) is diffrentiable if the following limit exists