## abz_tech 3 years ago f(x)' x√x

1. abz_tech

hmm?

$\Large \sqrt{x}=x^ \frac{1}{2}$Do you know this?

3. abz_tech

ya .. i know derivite of that is 1/2√x

The easier way is to do by this metho$\Large x \sqrt{x}= x.x^ \frac{1}{2}$

5. abz_tech

ok.. then?

$\Large x^m \times x^n = x^{m+n}$

$\Large x \times x^ \frac{1}{2}= ?$

8. annas

x^3/2

9. abz_tech

0_o.. didn;t think of that..but aren't u supposed to use roduct rule?

10. abz_tech

product rule

11. annas

no product rule is not applicable here 3/2 x^1/2 answer

12. abz_tech

now that makes sense 0_o

Yes you can use product rule ,You'll get the same answer

14. abz_tech

why not tough?

15. abz_tech

:o ok

16. abz_tech

thx

17. annas

$3/2x^{1/2}$

$\frac{d}{dx}x \sqrt{x}=x \frac{d}{dx}\sqrt{x}+\sqrt{x}\frac{d}{dx}x$$=x .\frac{1}{2\sqrt{x}}+\sqrt{x}=\frac{x}{2\sqrt{x}}+\sqrt{x} =\frac{\sqrt{x}}{2}+\sqrt{x}$$=\frac{\sqrt{x}}{2}+ \frac{\sqrt{x}}{1}=\frac{\sqrt{x}}{2}+\frac{\sqrt{x} \times 2 }{1 \times 2} =\frac{\sqrt{x}}{2}+\frac{2\sqrt{x}}{2}=\frac{3\sqrt{x}}{2}$

Using the Product Rule^^

20. annas

wow diya you are really good at maths :)

$\Large \frac{3}{2}x^ \frac{1}{2}= \frac{3}{2}\sqrt{x}= \frac{3\sqrt{x}}{2}$Same answer! :)

Lol Thanks Annas!

23. annas

welcome !

24. abz_tech

lol ye.. ur really good

25. abz_tech

hmm hey, if u dont mind can u help me with another question =/?

Post another question :)

27. abz_tech

ok