- #1

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1 .derivaive of y, y = x^a^x

2. nth derivaive of (x+p)^-1 p is constant

3. nth derivaive of (ax+b)/(cx+d)

4. nth derivaive of y = sin (^2) x

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- Thread starter mousesgr
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- #1

- 31

- 0

1 .derivaive of y, y = x^a^x

2. nth derivaive of (x+p)^-1 p is constant

3. nth derivaive of (ax+b)/(cx+d)

4. nth derivaive of y = sin (^2) x

- #2

HallsofIvy

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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.

- #3

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i know how to do qs 1

- #4

HallsofIvy

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

ln(y)= a

(You will need to use the chain rule on the left side and the product rule on the right.)

- #5

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HallsofIvy said:

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

ln(y)= a^{x}ln(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.)

i mean i know how to do the first one now

- #6

VietDao29

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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,

- #7

r3dxP

mousesgr said:

1 .derivaive of y, y = x^a^x

2. nth derivaive of (x+p)^-1 p is constant

3. nth derivaive of (ax+b)/(cx+d)

4. nth derivaive of y = sin (^2) x

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..

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