# Thread: Help with Derivatives

1. ## Help with Derivatives

I need some help solving these derivative problems:

1. F(x)= 3rd root of(x)-[1/3rd root of(x)]
For this one I got: 1/3 x - 3rd root of(9)

2. (s^2+s+1)^4 * (s-2)^7
I tried doing this one but it got out of hand and messy.

Any help would be great.

2. Before I work this through, tell me if this is what the equation is:
$\displaystyle x^3 - \sqrt[3]{x}$
and
$\displaystyle (s^2 + s + 1)^4 * (s-2)^7$

3. yep that's them.

For future reference how do you do that (make math symbols visible and all)

-thankx

4. Just use this tutorial: http://www.mathhelpforum.com/math-he...-tutorial.html

$\displaystyle f(x) = x^3 - {x}^\frac {1}{3}$

From here, you will want to use the power rule so:

$\displaystyle f'(x) = 3x^2 - \frac {x}{3}^ {\frac {1}{3} - 1} =$
$\displaystyle 3x^2 - \frac {x}{3}^ {\frac {-2}{3}}$

Now for the second you will need to use the chain rule and the product rule.

$\displaystyle f(x) = (s^2 + s + 1)^4 * (s-2)^7$

$\displaystyle f'(x) = (s^2 + s + 1)^4 * 7(s-2)^6 + (s-2)^7 * 8s(s^2 + s + 1)^3$

5. Originally Posted by JoshHJ
Just use this tutorial: http://www.mathhelpforum.com/math-he...-tutorial.html

$\displaystyle f(x) = x^3 - {x}^\frac {1}{3}$

From here, you will want to use the power rule so:

$\displaystyle f'(x) = 3x^2 - \frac {x}{3}^ {\frac {1}{3} - 1} =$$\displaystyle 3x^2 - \frac {x}{3}^ {\frac {-2}{3}}$

Now for the second you will need to use the chain rule and the product rule.

$\displaystyle f(x) = (s^2 + s + 1)^4 * (s-2)^7$

$\displaystyle f'(x) = (s^2 + s + 1)^4 * 7(s-2)^6 + (s-2)^7 * 8s(s^2 + s + 1)^3$
I think you might have meant $\displaystyle f({\color{red}s}) = (s^2 + s + 1)^4 * (s-2)^7$

and

$\displaystyle f'({\color{red}s}) = (s^2 + s + 1)^4 * 7(s-2)^6 + (s-2)^7 * {\color{red}4(2s+1)} (s^2 + s + 1)^3$.

6. Originally Posted by roksteady
yep that's them.

[snip]
Clearly not, since you re-posted the cube root one ....

Originally Posted by roksteady
5. $\displaystyle \sqrt[3]{x}-1/\sqrt[3]{x}$
I got: 1/3x^(-2/3) + 1/3x^(-4/3)