1. ## derivative q's

Find the derivative. State the domain of the function and the domain of its derivative.

f(x) = x + √x

f(x) = (3 + x) / 1-3x

Find F'(a)

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

f(x) = √3x + 1

2. Originally Posted by bballj228
Find the derivative. State the domain of the function and the domain of its derivative.

f(x) = x + √x

f(x) = (3 + x) / 1-3x

Find F'(a)

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

f(x) = √3x + 1
What's giving you trouble?

For the first, rewrite: $\displaystyle x + \sqrt x = x + x^{1/2}$ and use the power rule. The second can be done simply with the quotient rule.

The third can also be done with the quotient rule, but it would be easier to reduce the fraction (factor the numerator).

For the fourth, use the chain rule:

$\displaystyle \frac d{dx}\left[\sqrt{3x} + 1\right] = \frac d{dx}\left[(3x)^{1/2} + 1\right] = \frac12(3x)^{-1/2}\frac d{dx}\left[3x\right]$

3. ## Almost right

x^(1/2)+x^1=x^(1/2)*(1+x^(1/2)) not x^(3/2). Differentiate each term with the power rule, the factorization makes it more complicated.

4. Originally Posted by Reckoner
For the first, rewrite: $\displaystyle x + \sqrt x = x + x^{1/2} = x^{3/2}$
Last time I checked

$\displaystyle x^a+x^b\ne{x^{a+b}}$

5. Originally Posted by Mathstud28
Last time I checked

$\displaystyle x^a+x^b\ne{x^{a+b}}$
Ha ha! That's a pretty bad mistake. Maybe I was too tired to notice the addition symbol in there.