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Differentiation...

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squance:
Can someone please help me out with some differentiation???

I keep getting the wrong answers....

Find the derivative of the following:

y(x) = x/(x^2+1)^1/2

I got (x^2+1) - 2x/(x^2+1)^3/2 as the answer to the first one... but the answer is 1/(x^2+1)^3/2

h(x) = -3x/2(1-x^2)^1/4

Im screwed for the second one.,.....
the answer for the second one is 3/4(1-x^2)^-5/4(x^2-2)

I know how to do these but its messy but i keep getting them wrong.. we use quotient rule for both...I need a solution please.

ed_saifa:
Perhaps make it a negative power and then use the product rule?

Mao:


using the quotient rule



multiplying by on top and bottom:






second question:







then using the quotient rule again:



multiplying by on top and bottom:









tada :D

squance:
Thanks...:)

But now I have more difficult questions....Please help me!!!

For the following functions evalutate the first few derivatives f'(x), f''(x), F^(3) (x) and so on. Deduce the pattern and write down an expression for the nth derivative f^(n)x

a). f(x) = x^n (answer is n! = n x (n-1) x (n-2) x (n-3)...

b). f(x) = 1/3x^3 (answer is (-1)^n (n+2)!/(6x^(n+3)


Assuming g(x) is twice differentiable, that is, we can write down g'(x) and g''(x), write down expressions for f''(x) if:

a). f(x) = xg(x^2) (answer is 6xg'(x^2) + 4x^3g''(x^2)

b). f(x) = g(root x) (answre is rootx g'' (root x) - g'(root x)/(4x root x)

Mao:
part 1:

a)








so the overall pattern is (kth derivative):



which simplifies to:



so why is your answer like that... =S ?

*argh* do the rest 2morrow :)

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