MCQ
If $y = {x^{\sin x}},$ then ${{dy} \over {dx}} = $
- ✓${{x\cos x.\log x + \sin x} \over x}.{x^{\sin x}}$
- B${{y[x\cos x.\log x + \cos x]} \over x}$
- C$y[x\sin x.\log x + \cos x]$
- DNone of these
$\therefore$ ${{dy} \over {dx}} = {x^{\sin x}}\left[ {\frac{{\sin x + x\cos x{{\log }_e}x}}{x}} \right]$.
$={{x}^{\sin x}}\left[ \frac{\sin x+x\cos x{{\log }_{e}}x}{x} \right]$
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($A$) $f$ is discontinuous exactly at three points in $\left[-\frac{1}{2}, 2\right]$
($B$) $f$ is discontinuous exactly at four points in $\left[-\frac{1}{2}, 2\right]$
($C$) $g$ is $NOT$ differentiable exactly at four points in $\left(-\frac{1}{2}, 2\right)$
($D$) $g$ is $NOT$ differentiable exactly at five points in $\left(-\frac{1}{2}, 2\right)$