Finding various derivatives - Help!

Looks like homework to me. Is it?

The first one like you need to work with ln(y)= (a^x)ln x.

The others, just calculate two or three derivatives and see if you can spot a pattern.

 

Did you read what I wrote before?

For [tex]y= x^{(a^x)}[/tex], take the logarithm of both sides:

ln(y)= a^xln(x). Now differentiate both sides, with respect to x.
(You will need to use the chain rule on the left side and the product rule on the right.)

 

For #2, you can use: (a^b)' = b a^{b - 1}.
Then note that (x + p)' = 1.
For example: [tex]y' = \left( \frac{1}{x + p} \right)' = -\frac{1}{(x + p) ^ 2}[/tex]
[tex]y'' = (y')' = -\left( \frac{1}{(x + p) ^ 2} \right)' = 2\frac{1}{(x + p) ^ 3}[/tex]
So [tex]y ^ {(n)} \ = \ ?[/tex]
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For #3, you need to arrange [tex]\frac{ax + b}{cx + d}[/tex] into something like: [tex]C + \frac{A}{cx + d}[/tex], where C, and A = const.
Then you just do the same like #2.
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For #4, you can try to take 1st, 2nd, 3rd, 4th, ... derivative of the function and see the rule.
Note that 2sin(x)cos(x) = sin(2x).
Viet Dao,

 

1. ln y = a^x lnx
y'/y = [xa^(x-1)]lnx + [(1/x)a^x]
y' = y[[xa^(x-1)]lnx + [(1/x)a^x]]

2. -1(x+p)^-2
too lazyt to do the rest..