## Alice_Dump 3 years ago Ppl of the world.. here comes the Next question -..-

1. Alice_Dump

its about the definition of the derivative >>>

2. SmithsAccount

were all beaming with anticipation...

3. Alice_Dump

Apply the definition of the d derivative to compute $f \prime (x)$ where $f(x)=3x ^{2}+x-2$

4. rvgupta

6x+1

5. AravindG

6x+1

6. Alice_Dump

i know .. $f'(x)= 6x +1$ .. but my teacher said do it with details like long way to get this answer

7. Alice_Dump

-..- i don't know how

8. AravindG

i see well |dw:1349804778192:dw|

9. Alice_Dump

XD ur hand-writting is Funnie XP

10. AravindG

lim delta x tends to 0

11. SmithsAccount

ikr!

12. Alice_Dump

O_O sorry didn't mean to .. oops im sorry >> >_< sowwie

13. amorfide

you have a function of x F(X)=3x²+x−2 to differentiate you multiply the coefficient of the unknown by the power of the unknown and decrease the power of the unknown by 1 for example f(x)=x² f'(x)=2(1)x^2-1=2x so f(x)=x f'(x)=1(1)x^1-1=x^0=1 if you have f(x)=2x² f'(x)=2(2)x^2-1=4x does this help? |dw:1349804820461:dw|

14. AravindG

np @Alice_Dump did u get that ?

15. Alice_Dump

-..- ppl brb .. gemme 5 minutes i need to do something .

16. Alice_Dump

wait okie >_<

17. UnkleRhaukus

$f'(x)=2\times 3x^{2-1} +1\times x^{1-1}-0\times2x^{0-1}=6x +1$

18. rvgupta

2*3x^(2-1)+x(1-1)

19. satellite73

$f(x)=3x^2+x-2$ $f(x+h)=3(x+h)^2+(x+h)-2=3(x^2+2xh+h^2)+x+h-2$ $=3x^2+6xh+3h^2+x+h-2$ $f(x+h)-f(x)=3x^2+6xh+3h^2+x+h-2-(32x^2+x-2)$ $=6xh+h+3h^2$

20. rvgupta

2 being constant will disappear

21. satellite73

divide by $$h$$ and get $\frac{f(x+h)-f(x)}{h}=6x+1+3h$ take the limit as $$h\to 0$$ get $$6x+1$$

22. satellite73

you needed it done by hand right? not power rule it is a bunch of algebra, that is all only last step is calc, and that is taking the limit by replacing $$h$$ by $$0$$

23. AravindG

indeed @satellite73 has illustrated the given problem nicely with the formula i have given you ...i think that clears evrything

24. satellite73

question said "Apply the definition of the derivative to compute"

25. satellite73

@AravindG thanks

26. AravindG

yw :)

27. Alice_Dump

:} back ..

28. Alice_Dump

i got the question now :] thnx ppl ^_^'

29. Alice_Dump

heehehe