special functions - Integration error spotting

What have I done wrong? 

I have to evaluate the following integral:

$$\int\limits_0^\infty\int\limits_0^{2\pi} \phi(r^2)\delta'(r^2-a)\delta\left(\theta- \left(n+{1\over 2}\right){\pi\over 2}\right) r \; d\theta \;dr$$

My (wrong) working:

$\implies 4\int\limits_0^\infty \phi(x)\delta'(x-a){1\over 2}dx$ by letting $x=r^2$

$\implies -2\phi'(a)$

I should be getting the integral equalling $\phi(a)-\phi'(a)$.

Thank you.