# Differentiate this function

1. Mar 15, 2007

### afcwestwarrior

y=x^2+4x+3/square root x

i did this

s
x^2+4x+3) square root x/ sq x * sq x

sq x *x^2)+4x*sq x+ 3/1

Last edited: Mar 15, 2007
2. Mar 15, 2007

### afcwestwarrior

i made all the sq x equal 1/2x^-1/2
so what am i suppost to do, i know its suppost to be 3/2 sq x + 2/sqx - 3/2x sq x

3. Mar 15, 2007

### afcwestwarrior

any one can u help me

4. Mar 15, 2007

### hage567

I can't tell what the function is. Is the square root of x just with the 3, or is it the denominator to all of it?? Try to use brackets to make things clearer.

Is this it? $$y=(x^2+4x+3)/\sqrt{x}$$

5. Mar 15, 2007

### shifty101uk

Use the Quotient rule.

6. Mar 15, 2007

### afcwestwarrior

thats it, on this one u dont use the quotient rule, i could, but there's a way since square root of x is a negative number

7. Mar 15, 2007

### hage567

OK, I THINK i see what you're getting at here, but I don't understand why you are multiplying sq x * sq x. If you break up each term to be over sq x, you can just then simplify the x each term, and then take the derivative. This way you don't have to do the quotient rule, you are just taking the derivative of each term separately. That is the only way I can see getting the answer you say it is supposed to be.

8. Mar 16, 2007

### shifty101uk

Ok, Ive never heard of this other way but good luck

9. Mar 16, 2007

### wombat7373

so x is imaginary?

10. Mar 16, 2007

### seanistic

I am in calculus 1 as well so correct me if I'm wrong. I would approach this problem a different way. First off quotient rule is too messy for my liking, Id rather use the product rule. To do this:

Step 1: Bring the denominator up so you can use the product rule:

Since:
sqrt(x) = x^1/2 and 1/(x^1/2) = x^-1/2 you can move sqrt(x) to the top (moving the x^1/2 to the numerator makes the exponent negative)

The original function (x^2+4x+3)/sqrt(x) now equals (x^2+4x+3)*(x^-1/2)
Step 2: Now, using the product rule solve:
(x^2+4x+3)*(-1/2)(x^-3/2)+(x^-1/2)*(2x+4)
simplify:
-1(x^2+4x+3)/2(x^3/2)+(2x+4)/(x^1/2)
To get even denominators multiply the right side by 2x
(-x^2-4x-3)/2(x^3/2)+(4x^2+8x)/2(x^3/2)
simplify, giving the derivative:
(3x^2+4x-3)/(2x^3/2)

*edit* if you write this out you will understand it ALOT better, I havnt mastered how to do the coding yet.

Last edited: Mar 16, 2007
11. Mar 16, 2007

### iamlovelyboy

use this

use (a+b+c)/d = a/d + b/d + c/d

and then differentiate each term .

12. Mar 17, 2007

### HallsofIvy

Staff Emeritus
(x^4+ 4x+ 3)/sqrt(x)= (x^4+ 4x+ 3)/x^(1/2)= (x^4+ 4x+ 3)x^(-1/2) and you can use the product rule.

Is that what you meant about square root being "negative"?

13. Mar 20, 2007

### afcwestwarrior

yes thats what i meant

14. Mar 20, 2007

### afcwestwarrior

actually in this equation u use the power rule,

take 1/x^2= -1x^-2= -1/x^2

except the problem i posted looks different and is more confusing

15. Mar 20, 2007

### ZioX

Learn the quotient rule. The quotient rule is the simplified product rule.

16. Mar 20, 2007

### mathmuncher

If you want a simpler way, you could divide the equation (as in y= (x^2)/(x^.5) +4x/(x^.5) +(3x^0)/(x^.5), and simplify the exponents (subtract them). Then just use the general power rule to find the derivative.

17. Mar 21, 2007

### jing

iamlovelyboy's method avoids the quotient and the product rule

$$y=(x^2+4x+3)/\sqrt{x} =(x^2 + 4x + 3)x^{-1/2} = x^{3/2} + 4x^{1/2} + 3x^{-1/2}$$

now differentiate each term

Last edited: Mar 21, 2007
18. Mar 21, 2007

### mathmuncher

My bad, I didn't see iamlovelyboy's post.