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Differential Calculus> If f(x)= sin x and g(x)= sgn sin x {which...

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If f(x)= sin xand 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.

Jayank Singh Senger , 10 Years ago

Grade 11

1 Answers

Jitender Singh

Last Activity: 10 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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