MCQ
If $y = \sec ({\tan ^{ - 1}}x),$ then ${{dy} \over {dx}}$ is
- ✓${x \over {\sqrt {1 + {x^2}} }}$
- B${{ - x} \over {\sqrt {1 + {x^2}} }}$
- C${x \over {\sqrt {1 - {x^2}} }}$
- DNone of these
$= \sec ({\tan ^{ - 1}}x) \tan ({\tan ^{ - 1}}x) \cdot \frac{{1}}{{1 + {x^2}}}$
$ = \frac{{x}}{{1 + {x^2}}}\,.\,\sqrt {1 + {x^2}} = \frac{{x}}{{\sqrt {1 + {x^2}} }}$, $({\tan ^{ - 1}}x = {\sec ^{ - 1}}\sqrt {1 + {x^2}} )$.
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where $[x]$ denotes the greatest integer less than or equal to $x$. Let $f \circ:(-1,1) \rightarrow R$ be the composite function defined by $(f \circ g)(x)=f(g(x))$. Suppose $c$ is the number of points in the interval $(-1,1)$ at which $f \circ g$ is NOT continuous, and suppose $d$ is the number of points in the interval $(-1,1)$ at which $f \circ g$ is $NOT$ differentiable. Then the value of $c+d$ is. . . . .