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# Solve it, - Limit , continuity and differentiability - JEE Main-7

Number of points of non diffrentiability of $f(x)=\sin (\cos x) in (-\infty ,\infty )$ will be

• Option 1)

infinite

• Option 2)

0

• Option 3)

1

• Option 4)

2

Answers (1)
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As we have learned

Properties of differentiable functions -

The composition of a differentiable function is a differentiable functions.

-

$f(x)= \sin (\cos x)$

Let $g(x)= \sin x$  and $h(x)= \cos x$

then f(x) =g(h(x)) which is a composition of two diffrentiable function g(x) and h(x) so f(x) will also be diffrentiable

$\therefore$ No . of required points = zero

Option 1)

infinite

Option 2)

0

Option 3)

1

Option 4)

2

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