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

\[\begin{array}{1 1}(1)\sec\theta&(2)\sin\theta\\(3)\cos\theta&(4)cosec\theta\end{array}\]

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$x= r \cos \theta$
$y= r \sin \theta$
$x^2+y^2=r^2 \cos ^2 \theta+ r^2 \sin^2 \theta$
$x^2+y^2= r^2$
D.w.r.t
$2x= 2r \large\frac{\partial r}{\partial x}$
$\large\frac{\partial r}{\partial x} =\frac{x}{R} = \frac{r \cos \theta}{r}$$=\cos \theta$
hence 3 is the correct answer.
answered May 20, 2014 by meena.p
 

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