## anonymous 5 years ago what is the derivative of: 2 square x (not sure how to do) and (1-2x)/x^3 I get 3x^3(-1+2x) not sure if correct

1. anonymous

sorry for the last one my answer is 3x^2(-1+2x)

2. anonymous

u can rewrite square of x by x^1/2

3. anonymous

2(sq.x)=2(x^1/2)

4. anonymous

multiply the exponent by the degree and subtract 1 from the exponent

5. anonymous

$2\sqrt{?}$ sorry I can't get it in corrrectly the ? should be the x

6. amistre64

take the 2 out and derive sqrt(x); or x^(1/2) 1/2sqrt(x) now put the 2 back in: 2/2sqrt(x) = 1/sqrt(x)

7. amistre64

(1-2x)/x^3 use quotient rule :) x^3(-2) - (1-2x)(3x^2) -------------------- x^6

8. anonymous

$\frac{d}{dx}[ \frac{(1-2x)}{x^3}]$ $= \frac{d}{dx}[ (1-2x)x^{-3}]$ $= (1-2x)\frac{d}{dx}[ x^{-3}] + x^{-3}\frac{d}{dx}[ (1-2x)]$ $= (1-2x)(-3x^{-4}) + x^{-3}(-2)$ $= -3x^{-4} + 6x^{-3} - 2x^{-3}$ $= \frac{4x-3}{x^4}$

9. amistre64

-2x^3 -3x^2+6x^3 4x^3 - 3x^2 (4x-3)x^2 -------- x^4 x^2 4x-3 ----- maybe?? x^4

10. anonymous

thanks, i have to go for now , i will check back in about and hour

11. amistre64

polpak did it good :) or we messed up toghter lol

12. anonymous

I prefer to ignore the quotient rule and use product rule with a negative exponent.

13. amistre64

potato<>potato :)

14. anonymous

I thought potato = potato ;p

There is another way to look at mom. (1-2x)/x^3 can be rewritten to appear as (1-2x)(x^-3) $(1-2x) *x ^{-3}=x ^{-3}-2x ^{-2}$

This may be in a more familiar form you can now simply take the derivative to be: $-3x ^{-4}+4x ^{-3}$ simplifying will obtain the results of polpak and amistre64