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If f(x)= sin x and g(x)= sgn sin x {which is signum of sinx) Then what is the value of: g’(1)? The answer is not 0. Can you also please show me the steps that lead to the final solution.

If f(x)= sin x
and g(x)= sgn sin x
{which is signum of sinx)
 
Then what is the value of:
g’(1)?
The answer is not 0. Can you also please show me the steps that lead to the final solution.

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Hello student, please find answer to your question
f(x) = sin(x)
g(x) = sgn(sin(x))
=1, sin(x) > 0
=0, sin(x) = 0
=-1, sin(x) < 0
Let take the interval 0 to 2pi
g(x)=1, 0 < x < \pi
=0, x = 0, \pi , 2\pi
=-1, \pi < x < 2\pi
g'(x)=0, 0 < x < \pi
=0, x = 0, \pi , 2\pi
=0, \pi < x < 2\pi

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