Posted by **Ann** on Thursday, October 31, 2013 at 2:38am.

Let f(x) = [(√x)-7]/[(√x)+7]. What is f'(x)?

What is the easiest way to find the derivative of this? Should I remove all the radicals and use quotient rule, like

f'(x)= ((x^0.5) + 7)(0.5x^-0.5) - ((x^0.5)-7)(0.5x^-0.5) / ((x^0.5) + 7)^2

Is this right? How do I simplify this? please show me thanks

- Pre-Calculus -
**Steve**, Thursday, October 31, 2013 at 5:00am
Radicals or exponents. Tomato, tomahto. Either way, it's slightly messy, but simplifies rather nicely.

f = (√x-7)/(√x+7)

As you say,

f' = (1/2√x)(√x+7)-(√x-7)(1/2√x))/(√x+7)^2

= (7/√x)/(√x+7)^2

= 7/[√x(√x+7)^2)

- Pre-Calculus -
**Ann**, Saturday, November 2, 2013 at 5:21pm
thank you

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