## calyne 3 years ago Differentiate the function y = ln |2-x-5x^2|

1. DHASHNI

is the ques correct?

2. calyne

yup

3. calyne

oops

4. calyne

fixed it

5. calyne

...

6. amistre64

$[ln(u)]'=\frac{u'}{u}$

7. calyne

what are those brackets or ||

8. calyne

because it's not |lnu| it's ln|u|

9. amistre64

those are just for grouping; it means that the whole of it is derived and not just the (u) part

10. calyne

okay so show me how

11. amistre64

i believe it goes piece wise in the end

12. amistre64

or you can use the sqrt(u)^2 trick

13. calyne

14. DHASHNI

|dw:1334421083017:dw|

15. amistre64

$\frac{d}{dx}ln(\sqrt{u\ }^2)=\frac{(\sqrt{u\ }^2)'}{ \sqrt{u\ }^2}\to\ \frac{2\sqrt{u\ }*\sqrt{u}'}{ \sqrt{u\ }^2}$

16. amistre64

if i follow that derivatives i think it would look like this ... but best to check with the wolf

17. amistre64

http://www.wolframalpha.com/input/?i=derivative+ln+%7C2-x-5x%5E2%7C the wolf doesnt seem to go thru the hoopla tho

18. amistre64

$\frac{2\sqrt{u\ }}{ \sqrt{u\ }^2}\sqrt{u}'$ $\frac{2\sqrt{u\ }}{ \sqrt{u\ }^2}\frac{u'}{2\sqrt{u}}=\frac{u'}{ \sqrt{u\ }^2}\to\ \frac{u'}{ |u|}$

19. calyne

whatevr it's 1/(2-x-5x^2) * -(10x+1) = 10x+1 / 5x^2+x-2 woohoo