# Math Help - differentiating.

1. ## differentiating.

okay, i have made a list of the problems i couldn't do from my textbook. would anyone be able to show complete and easy to understand working out for why the answers are what they are?

differentiate the following:

$y(x) = \frac{16}{25}(x+\frac{1}{x})^3$
$f(x)= \frac{-sinx^2}{\sqrt{x}}$
$f(x)= 4xloge_{e}(3x)$
$f(x)= 3(1-x^2)sin(x)$

any help will be appreciated!

2. 1. $y(x) = \frac{16}{25}(x+\frac{1}{x})^3 = y(x) = \frac{16}{25}(x+x^{-1})^3$

$y'(x) = 3. \frac{16}{25} (x + x^{-1})^2 . (1 - x^{-2})$

I 'lowered' the power and multiplied it to the curve, then decreased the power by one, without changing the part in brackets. Then, I multiplied the whole thing by the derivative of the part in brackets. Now, you can simplify.

For the second, use the quotient rule and for the last two, use the product rule. Post what you get!

3. Originally Posted by Mr Rayon
okay, i have made a list of the problems i couldn't do from my textbook. would anyone be able to show complete and easy to understand working out for why the answers are what they are?

differentiate the following:

$y(x) = \frac{16}{25}(x+\frac{1}{x})^3$
$f(x)= \frac{-sinx^2}{\sqrt{x}}$
$f(x)= 4xloge_{e}(3x)$
$f(x)= 3(1-x^2)sin(x)$

any help will be appreciated!
$\displaystyle (u \pm v)'=u' \pm v '$

$\displaystyle (u \cdot v)'=u' \cdot v + u \cdot v'$

$\displaystyle (\frac{ u}{v})' = \frac {u' \cdot v-u \cdot v'}{v^2}$

and any combination of those

of course you need to know (here at least) by heart maybe 30 or less table derivation and you will have no problems to solve that up there (or any another) using basic principles

4. Please, I still need help with the rest.

5. It would help if you gave it a try and showed us, and tell us where you get stuck.
Learn the quotient, product and chain rule if you don't know what they are to solve the equations.

Unknown008 has told you which rules to use and yeKciM has given you the rules for differentiating them.

It is better to learn those rules and attempt the equations and show us what you did rather than just asking others for the working out and answers.