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# Differentaiation

i need help in Differentaiation but by using definition exampel 6.x i need steps

### 2 Answers by Expert Tutors

Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.
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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).

LOL:  We need to constantly remind our students to write clearly.  I don't think he meant abs(6x), but I'm not sure what "6.x" means - probably just multiplication ---->  6x
Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
4.6 4.6 (8 lesson ratings) (8)
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As per definition

differentiation of f(x)= f'(x) = Limit h>0 (f(x+h) - f(x))/h ................ Limit h tends to zero

Therefore

f'(6x) = Limit h>0 (6(x+h) - 6x)/h

=> (6x + 6h - 6x)/h.................. limit h tends to zero

=> 6h/h = 6

:)