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

PreCalculus  Steve, Thursday, October 31, 2013 at 5:00am
Radicals or exponents. Tomato, tomahto. Either way, it's slightly messy, but simplifies rather nicely.
f = (√x7)/(√x+7)
As you say,
f' = (1/2√x)(√x+7)(√x7)(1/2√x))/(√x+7)^2
= (7/√x)/(√x+7)^2
= 7/[√x(√x+7)^2)

PreCalculus  Ann, Saturday, November 2, 2013 at 5:21pm
thank you
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