# Math Help - Differentiate the following

1. ## Differentiate the following

i havn't done maths in awhile and when i got back into it ive totally forgot how to do these so if anyone could help me out it will be great

so differentiate the following and simplify where appropriate

y= x^5/(3x+4)

y = lnx/x

r(t) = ln(2t square root (t + 1))

thanks

2. Originally Posted by helpme2009
i havn't done maths in awhile and when i got back into it ive totally forgot how to do these so if anyone could help me out it will be great

so differentiate the following and simplify where appropriate

y= x^5/(3x+4)

y = lnx/x

r(t) = ln(2t square root (t + 1))

thanks
For the first one you will need the quotient rule:
$\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}$
In this case $f(x)=x^5$ and $g(x)=3x+4$

Then we have:
$\frac{d}{dx}\frac{x^5}{3x+4}=\frac{(5x^4)(3x+4)-(x^5)(3)}{(3x+4)^2}=...$
The rest is just simplifying.
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The second one is similar to the first one. You can do this problem using the quotient rule.
(Note also: $\ln x=\frac{1}{x}$)

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The third one is a combination of the chain rule and the product rule or by changing it a little bit can avoid the chain rule. (I assume that you know these two rules?)