If $y = {\sec ^{ - 1}}\left[ {{\rm{cosec}}x} \right] + {\rm{cose}}{{\rm{c}}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],$ then $\frac{{dy}}{{dx}}$ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

then

\frac{{dy}}{{dx}}

is equal to

View answer and explanation

Correct option: D

- 4

Option D (-4) is correct because after simplifying the expression using trigonometric identities, the derivative is found to be -4.