differentiation questions

• Sep 27th 2009, 02:45 PM
jayjay60
differentiation questions??? :(
HELP PLEASE! there's a time limit to this. it's homework, not a quiz. but i have tried and tried. i'm dead serious. :(

can you guys help?

Differentiate the following function. http://www.webassign.net/cgi-bin/sym...x%29%29%29%5E2
would i foil and then differentiate? because i've tried that over and over.

and then another:

Differentiate. http://www.webassign.net/cgi-bin/sym...%5E%281%2F3%29
(honestly, i don't understand why i can't get THAT one..i get the same answer over and over.... ((32/3)t^1/3) - ((5/6)t^-1/6)...errggggg :(

i'm sorry. i'm not usually a questions person. but i am highly interested in calculus. please help??
• Sep 27th 2009, 03:05 PM
DeMath
Quote:

Originally Posted by jayjay60
i have tried and tried. i'm dead serious. :(

can you guys help?

Differentiate the following function. http://www.webassign.net/cgi-bin/sym...x%29%29%29%5E2
would i foil and then differentiate? because i've tried that over and over.

and then another:

Differentiate. http://www.webassign.net/cgi-bin/sym...%5E%281%2F3%29
(honestly, i don't understand why i can't get THAT one..i get the same answer over and over.... ((32/3)t^1/3) - ((5/6)t^-1/6)...errggggg :(

i'm sorry. i'm not usually a questions person. but i am highly interested in calculus.

For 1

$u = {\left( {5\sqrt x + \frac{6}
{{5\sqrt[3]{x}}}} \right)^2} \Rightarrow \frac{{du}}
{{dx}} = \frac{d}
{{dx}}{\left( {5\sqrt x + \frac{6}
{{5\sqrt[3]{x}}}} \right)^2} =$

$= 2\left( {5\sqrt x + \frac{6}
{{5\sqrt[3]{x}}}} \right) \cdot \frac{d}
{{dx}}\left( {5\sqrt x + \frac{6}
{{5\sqrt[3]{x}}}} \right) =$

$= 2\left( {5\sqrt x + \frac{6}
{{5\sqrt[3]{x}}}} \right)\left[ {\frac{d}
{{dx}}\left( {5\sqrt x } \right) + \frac{d}
{{dx}}\left( {\frac{6}
{{5\sqrt[3]{x}}}} \right)} \right] =$

$= 2\left( {5\sqrt x + \frac{6}
{{5\sqrt[3]{x}}}} \right)\left( {\frac{5}
{{2\sqrt x }} - \frac{2}
{{5\sqrt[3]{{{x^4}}}}}} \right) =$

$= 25 - \frac{4}
{{\sqrt[6]{{{x^5}}}}} + \frac{6}
{{\sqrt[6]{{{x^5}}}}} - \frac{{24}}
{{25\sqrt[3]{{{x^5}}}}} =$

$= 25 + \frac{2}
{{\sqrt[6]{{{x^5}}}}} - \frac{{24}}
{{25\sqrt[3]{{{x^5}}}}}.$
• Sep 27th 2009, 03:11 PM
jayjay60
oh wow!

this question was in my sctn 3.3 hwk.
we learned THAT formula in 3.4.

oh man, i was so confused.
but seriously.

i honestly praise you. you're my favorite person ever atm. <3
• Sep 27th 2009, 03:31 PM
DeMath
Quote:

Originally Posted by jayjay60
HELP PLEASE! there's a time limit to this. it's homework, not a quiz. but i have tried and tried. i'm dead serious. :(

can you guys help?

Differentiate the following function. http://www.webassign.net/cgi-bin/sym...x%29%29%29%5E2
would i foil and then differentiate? because i've tried that over and over.

and then another:

Differentiate. http://www.webassign.net/cgi-bin/sym...%5E%281%2F3%29
(honestly, i don't understand why i can't get THAT one..i get the same answer over and over.... ((32/3)t^1/3) - ((5/6)t^-1/6)...errggggg :(

i'm sorry. i'm not usually a questions person. but i am highly interested in calculus. please help??

For 2

$g\left( t \right) = \frac{{8t - \sqrt t }}
{{{t^{1/3}}}} = 8{t^{2/3}} - {t^{1/6}} \Rightarrow$

$\Rightarrow \frac{d}
{{dx}}g\left( t \right) = \frac{d}
{{dx}}\left( {8{t^{2/3}} - {t^{1/6}}} \right) =$

$= \frac{{16}}
{3}{t^{ - 1/3}} - \frac{1}
{6}{t^{ - 5/6}} = \frac{{16}}
{{3{t^{1/3}}}} - \frac{1}
{{6{t^{5/6}}}}.$