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$If f (x) = \{\begin{array}{cc} 1, & x < 0 \\ 1 + \sin x, 0 \leq x < \frac{π}{2}, Then f^{'} (0) i s \end{array}$

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does not exist

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Correct option is B

L.H.D. at x=0 is ddx1x=0=0R.H.D at x=0 isddx1+sinxx=0=cos0=1.∴f'x does not exist.

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If f(x)=1,x<01+sin⁡x,0≤x<π2, Then f′(0)is

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$If f (x) = \{\begin{array}{cc} 1, & x < 0 \\ 1 + \sin x, 0 \leq x < \frac{π}{2}, Then f^{'} (0) i s \end{array}$