Expert: Scotto - 7/10/2008

Question
QUESTION: sir
how can i find the derivative of x raise to the power 5/2 by definition method? actually this problem can be easily solved by simple power rue but by definition i m not able to calculate (x - delta x) raise to the power 5/2.Can you please help me?

ANSWER: To raise a number to the x to the 5/2 power, take the squareroot and raise it to the 5th power.  4^(5/2)=2^5=32; 9^(5/2)=3^5=243.

It could also be said that 5/2 is 2.5.  Thirds aren't quite so trivial (1/3=0.333333333333...), but 1/4=0.25, 1/5=0.2, and 1/8=0.125.

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QUESTION: thanks .but sir i want to find derivative of x to the power
5/2 by ab initio method.can you solve it for me

Answer
I'm not entirely sure what, 'derivative of x to the power
5/2 by ab initio method.can you solve it for me' means, but it might be finding d(x^(5/2))/dx.  d(x^(5/2))/dx = 5/2(x^(3/2)) since
3/2 = 5/2 - 1.

Note that the derivative d(x^y)/dx = yx^(y-1) for any real value of y.

To find it, use Excel and put x in A3, put =A3^2.5 in A4, and put =5*A3^1.5/2 in A5.  To get the answer, put the proper value for x in A3.  A2 will have f(x) and A3 will have f'(x).

To go more into depth, put x0 in A1, delta in A2, and =A1+A2 in A3.  A1 will not have the value of x we are taking the limit to, A2 will have how much of a difference there is (+ or -), and A3 will have the value near x.

Hope this answers your question.