Hilbert Space Help!

How can I show that the space of all continuously differentiable functions on [a,b] denoted W[a,b] with inner product (f,g)=Integral from a to b of (f(x)*conjugate of g(x)+f'(x)*conjugate of g'(x)).

Should I show that the norm does not satisfy the parallelogram law?

Gokul43201
Staff Emeritus
$$\langle f,g \rangle = \int _a ^b (fg^* + f'g'^*)dx$$ ?