Tuesday

September 2, 2014

September 2, 2014

Posted by **Angie** on Saturday, September 22, 2012 at 10:45am.

Differentiate the following using the chain rule.

f(x) = squareroot(x^2+1)/(3x+1)

I know that I can take the whole thing and put it to the (1/2) and differentiate that then use the quotient rule to differentiate the inside, but when i try to factor I can't get stuck. with 3x^2+2x-3/(3x+1)^2

- Calculus -
**Steve**, Saturday, September 22, 2012 at 3:43pmassuming you mean

f(x) = √((x^2+1)/(3x+1))

f = u^1/2 where u = (x^2+1)/(3x+1)

so,

f' = 1/2√u u'

u = f/g where

f = x^2+1 and v = 3x+1

so, u' = (f'g-g'f)/g^2 = (3x^2+2x-3)/(3x+1)^2

so f' = 1/[2√((x^2+1)/(3x+1))] * (3x^2+2x-3)/(3x+1)^2

= (3x^2+2x-3)/[2(3x+1)^{3/2}(x^2+1)^{1/2}]

**Answer this Question**

**Related Questions**

calculus - I am having trouble with this problem also derivative differentiate f...

calculus - Using the chain rule... how can i differentiate this? y=x(x-2)

calculus - I have been asked to solve this two different ways. The first way is...

Calculus - Differentiate using the chain rule: y=(x+(x+x^(1/2))^(1/2))^(1/2) y...

Calculus - How do I use the chain rule to find the derivative of square root(1-x...

Calculus - Derivative Differentiate f(x)=(5x-4)^2 There are two ways to do this...

calculus 1 - differentiate x(x-3)^2 do I product and chain rule?

MoRe HeLp PlEaSe!! (calc) - Also can I get some help with this LONG, TIRESOME ...

Calculus - Find the derivative of f(x) =cos^-1(x^2) Ok so I'm having a little ...

maths - differentiate using product, chain and quotient rule ln x / 5x-7 and e^x...