## roselin 3 years ago find the derivative of u=5x+1/2 sqrt of x

1. Lexxiie123

what is sqrt

2. Lexxiie123

is it square root?

3. roselin

yes

4. mark_o.

derivative of u=5x+(1/2) sqrt of x sometimes its easier to use the power rule, and rewriting it as u=5x+(1/2 )( x)^1/2 use power rule of the derivative

5. mark_o.

d(kx)/dx=k.,,dx^n/dx= nx^n-1

6. roselin

the problem is actually: |dw:1351567010524:dw|

7. mark_o.

u=5x + 1/(2sqrtx)?

8. roselin

$u= 5x+1\div 2\sqrt{x}$

9. mark_o.

it will be the same idea by using the power rule u=5x + 1/(2sqrtx) u=5x + (1/2)(x)^-1/2 now find the derivative

10. roselin

what if i use the quotient rule?

11. mark_o.

u=5x + (1/2)(x)^-1/2 is it du/dt=5+(1/2)(-1/2)x^-1/2 - 2/2) du/dt=5+(1/2)(-1/2)x^-3/2 ) ?

12. roselin

its find the derivative of the function $u= 5x+1 \div \sqrt{2}$

13. mark_o.

ok the quotient rule says $\frac{ d(\frac{ U }{ V }) }{ dx }=\frac{ V \frac{ du }{ dx }-U \frac{ dV }{ dx } }{ v ^{2} }$

14. roselin

$u= 5x+1\div 2\sqrt{x}$

15. roselin

so i must use the power rule?

16. mark_o.

arrange them like $u=5x +(\frac{ 1 }{ 2 })(\frac{ 1 }{ x ^{\frac{ 1 }{ 2 }} })$

17. roselin

okay

18. mark_o.

what did you get ?

19. roselin

give me a minute

20. mark_o.

lets try to work only on 1/x^1/2

21. mark_o.

u=1, v=x^1/2

22. roselin

where did u get the v from?

23. mark_o.

if you are using the quotient rule Dx(U/V)

24. roselin

wait the quotient rule is |dw:1351568697070:dw|

25. roselin

that is the quotient rule right?

26. mark_o.

lets try to work only on 1/x^1/2 therefore Dx(U/V)=Dx( 1/x^1/2) so here u=1 and v=x^1/2

27. roselin

its 2

28. roselin

sorry,

29. mark_o.

yes on youR formula g=V..,f=u , its the same..you guys have taught f and g but variables such u,v, w are used also locally and internationally

30. roselin

okay,

31. mark_o.

ok try to use your formula and you will arrive with the same answer anyway

32. roselin

i am solving it here, give me a minute i will post what i have

33. mark_o.

34. roselin

$-5x+6/ 2\sqrt{x}$

35. roselin

36. roselin

u thre?

37. mark_o.

hm try to study this one let u=1 and v= x^1/2 Dx(1/(x)^1/2) x^1/2(Dx(1) - 1 Dx(x^1/2) = --------------------------- ( x^1/2)^2 0 - (1/2)x^-1/2 = ---------------- x -(1/2) = --------- x x^1/2 -(1/2) =-------------- x^3/2 -1 = ---------- 2 x^3/2

38. mark_o.

now lets go back to the prob derivative of u=5x+(1/2)( x)^1/2 1 du/dx= 5 - ------------ 2( 2x^3/2) 1 = 5- ------------- 4x^3/2 w/c is the same as doing it w/ power rule