Question

Find the derivative of: f(x)=[ x^(1/2)+1]/[x^2 + 1]

Answer 1

use the power rule,
for 1/x^2
use this: and then the power rule
\[\large \frac{ 1 }{ x^n } = x^{-n}\]
the derivative of a constant is zero.

Answer 2

Thank you, so you're splitting them up? & for some odd reason, what you wrote isn't showing up :/

Answer 3

oh, I think it's because OpenStudy isn't showing LaTeX for everyone.

Answer 4

f(x) = x^(1/2) + x^(-2) + 1
power rule is
f(x) = x^n
f'(x) = nx^(n-1)

Answer 5

Ohhhh, I get what you did. You're making it all one line instead of using the quotient rule right?

Answer 6

all you do is differentiate each value with respect to x . so
f(x) = x^(1/2) + x^(-2) + 1
f'(x) = d/dx (x^(1/2) + d/dx (x^(-2)) + d/dx (1)

yeah, i find it easier than having to use the quotient rule.

Answer 7

Okay thank you

Answer 8

x^-n = 1/x^n
x^-2 = 1/x^2
np