Ask Me Help Desk - Find the derivative of the following:

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find the derivative of the following:

can someone help please

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

The derivative of a quotient is found using the following rule:

For
$ f(x) = \frac {g(x)} {h(x)} $
The derivative f'(x) is found by:
$ f'(x) = \frac{ h(x)g'(x)-g(x)h'(x)} {([h(x)]^2} $

For your problem:

$g(x) = x^2$ and $h(x) = \sqrt {x^2+1}$ .

Post back if you have more questions on this.

You can also use the product rule on this by writinf it as

$\underbrace{x^{2}}_{\text{f(x)}}\overbrace{(x^{2}+ 1)^{\frac{-1}{2}}}^{\text{g(x)}}$

The product rule is $f(x)g'(x)+g(x)f'(x)$

I always thought it was easier to use the product rule if one can.

Yup, its shorter and does not require the squared of the second term.

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