यदि `y= tan ^(-1) ((acos x- bsin x )/(b cos x+asin x )),` तब ` (dy)/(dx)` का मान ज्ञात कीजिए|

Explanation

यहाँ ` y= tan ^(-1) ((acos x-b sin x)/(b cos x+ a sin x))`
तब ` a=r sin theta ` तथा ` b=r cos theta,` तब
` y= tan ^(-1) { (r(sin theta cosx -cos theta sin x ))/(r(cos theta cos x +sin theta sin x ))}`
` =tan ^(-1) {(sin (theta -x))/(cos(theta -x))}=tan ^(-1) {tan (theta -x)}`
` y= (theta -x) =(tan ^(-1)""(1)/(b) -x)`
`(dy)/(dx) =(d)/(dx) (tan ^(-1) ""(a)/(b) -x)=0-1`
` (dy)/(dx) =-1`