The derivative of the function, $f(x) = {\cos ^{ - 1}}\left\{ {\frac{1}{{\sqrt {13} }}} \right.(2\cos x - 3\sin x)\} {\rm{ }} + {\sin ^{ - 1}}\left\{ {\frac{1}{{\sqrt {13} }}(2\cos x + 3\sin x)} \right\}$ ${\rm{ w}}{\rm{.r}}{\rm{.t}}{\rm{.}}\,\,\,\sqrt {1 + {x^2}} \,\,\,{\rm{at}}\,\,\,x = \frac{3}{4}\,\,{\rm{is}}$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Analyzing +4 | -1

The derivative of the function,

f(x) = {\cos ^{ - 1}}\left\{ {\frac{1}{{\sqrt {13} }}} \right.(2\cos x - 3\sin x)\} \mathrm{ } + {\sin ^{ - 1}}\left\{ {\frac{1}{{\sqrt {13} }}(2\cos x + 3\sin x)} \right\}

\mathrm{ w}\mathrm{.r}\mathrm{.t}\mathrm{.}\,\,\,\sqrt {1 + {x^2}} \,\,\,\mathrm{at}\,\,\,x = \frac{3}{4}\,\,\mathrm{is}

View answer and explanation

Correct option: C

\frac{10}{3}

Option C (

\frac{10}{3}

) is correct because after simplification and differentiation, the value of the derivative at

x = \frac{3}{4}

\frac{10}{3}