36. Put

then

To find the Differential Coefficient of cot x.

y cot x, y + dy = cot (x + dx);

=

sin Sx

бх

To find the Differential Coefficient of sec x.

37. Putting y = sec x, y + dy = sec (x + dx),

To find the Differential Coefficient of cosec x. 38. Putting y = cosec x, y + dy y + dy = cosec (x + dx),

To find the Differential Coefficient of sin x with regard to x.

Now, proceeding to the limit, when dx and dy assume values less than any assignable magnitudes, we have

To find the Differential Coefficient of tan`1 x.

41. Proceeding in the same way as in the investigation of the differentials of sin1x and cos x, we have

or

y tan1x,

=

y + dy = tan1 (x + dx),

tan y = x, tan (y+dy): = x + dx,

Extan (y+dy) - tan y

sin (y+dy). cos y sin y. cos (y + dy)

42.

To find the Differential Coefficient of cot1 x.

y = cot1 x, y + dy = cot1 (x + dx),