Question

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

Answer 1

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)

Answer 2

thank you