Question

$x=r\cos \theta ,y=r\sin \theta$, then $\frac{\partial r}{\partial x}$ is equal to:

• A. $\sec \theta$
• B. $\sin \theta$
• C. $\cos \theta$
• D. $\text{cosec}\theta$

Answer 1

The correct option is A $\sec \theta$

$x=r\cos \theta$ or $r=x\sec \theta$.
Hence
$\frac{\partial r}{\partial x}=\frac{\partial \left(x\sec \theta \right)}{\partial x}$

$=\sec \theta$.