# Math Help - Differentiation

1. ## Differentiation

determine f'(x) of f(x) = [4rt(x2+4)]^3
dy/dx of:
y=x^2(x-3)^5
y=3x(x+1)^3+3
y=2x(x^2+3)^4

The isosceles triangle has sides AC and AB of equal length and each increasing at 0.1cm/sec from an initial 5cm. Find the rate of change in the area of triangle ABC at the instant when AC=AB=10cm.

The length of a particular rectangle is three times its width and this ratio is maintained as the width is increased at 1mm/sec. Find the rate of increase in the area of the rectangle when the width is 10cm.

A right angle triangle has sides AB and BC able to vary in length, AC is constantly 10cm long and angle ABC is always a right angle. Initially AB is of length 4cm and increases at a constant rate of 0.1cm/sec. Find the rate of change in the length of BC, 20 seconds after the increasing in the length of AB commenced.

2. Originally Posted by Mickey

determine f'(x) of f(x) = [4rt(x2+4)]^3
dy/dx of:
y=x^2(x-3)^5
y=3x(x+1)^3+3
y=2x(x^2+3)^4
People here at MHF are not fond of those who post a whole bunch of questions piled up into one post. I will start off by helping you with the chain rule for the first of these questions. With that, you should be able to do the 2nd, 3rd and 4th problems.

$f(x) = [4rt(x^2+4)]^3$

Apply the chain rule when deriving this function.

$f'(x)=3[4rt(x^2+4)]^2 * ???$

Those question marks are to be filled with what you are supposed to tack on for the chain rule. When a function has functions nested in it like so: $f=g(h)$, then the derivative follows through like a chain: $f'=g'(h)*h'$

Therefore....

$f'(x)=3[4rt(x^2+4)]^2 * ??? \Rightarrow 3[4rt(x^2+4)]^2 4rt(2x) = 24rtx[4rt(x^2+4)]^2$

Remember one last thing here; you are deriving with respect to x. Other variables are then treated as constants, hence why the "r" and "t" followed through as coefficients.

3. Originally Posted by colby2152
People here at MHF are not fond of those who post a whole bunch of questions piled up into one post. [snip]
Hmmmmmm, not to mention a lack of thanks for any of the replies given to date.

4. Hi,

...and people who just ask their question then never come back :'(