Okay I'm not sure if this is University level or below, but anyway

Apply the Leibnitz theorem to the function

and hence prove that,

Now I can easily prove this using the Binomial theorem as the terms on the LHS are merely squares of the binomial coefficients in the expansion

And the RHS is the coefficient of in the expansion of

Using this data the above relation can be proved easily.

But I am not able to prove it using the method the question demands, that is, by using the Lebnitz formula for derivative of a function.

Can anyone help?