i need help in Differentaiation but by using definition exampel 6.x i need steps
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This is not a monotonic smooth function. If f(x)=I6xI, then you have to distinguish two domains: x< 0 when
f(x) =- 6x, and x > 0 when f(x) = 6x.
Thus, f'(x) = -6 for x<0 and f'(x) = 6 for x > 0
The derivative f'(x) is not a continuous function because there is no derivative at x=0
(the graph of f(x) =I6xI is broken at x = 0).
As per definition
differentiation of f(x)= f'(x) = Limit h>0 (f(x+h) - f(x))/h ................ Limit h tends to zero
f'(6x) = Limit h>0 (6(x+h) - 6x)/h
=> (6x + 6h - 6x)/h.................. limit h tends to zero
=> 6h/h = 6