Prove that the extremity of the polar subtangent of the curve $u+f(\theta)=0$ is $u=f'(\theta+\frac{\pi}{2})$ where $u=\frac{1}{r}$

Question

Prove that the extremity of the polar subtangent of the curve

$$u+f(\theta)=0$$ is $$u=f^{\prime} \left(\theta+\frac{\pi}{2} \right)$$ where $u=\frac{1}{r}$

I am confused and I think that it should be $$u=f^{\prime} \left(\theta-\frac{\pi}{2} \right)$$

Please Help me out !