Math Is Fun Forum

((1/square root x) - (square root x))^3

Let us take y = ((1/square root x) - (square root x))^3

On simplifying, we will get...

         y = x^(-3/2) - 3x^(-1/2) + 3x^(1/2) -x^(3/2)
         

Differentiate with respect to x, we will get.

         dy/dx = (-3/2)x^(-5/2) + (3/2)x^(-3/2) + (3/2)x^(-1/2) - (3/2)x^(1/2)

On simplifying

         dy/dx = 3/2(-x^(-5/2) + x^(-3/2) + x^(-1/2) - x^(1/2))

Let me know, if there is any correction in my steps.

  With regards
    Moses

What is the difference between sequence and pattern? Can any one help me to get a clear picture?
I need to take a presentation on this tomorrow, so please help its urgent.

With regards
Moses

Victoria woke up in the middle of the night and looked at her digital clock, it said 2:58, then she saw it change to 2:59 and then 3:00. Bored she began adding up the digit as they changed 15,16.3. Hmmmm
At 3:01 the digit added up to 4. A minute later the sum was 5. Victoria liked the pattern. She turned on the light and began figuring. She found that of all the digit sums on a 12 hour digital clock only one is unique meaning there is only one time that give you that sum.

What is the unique digit sum, and what is it's corresponding time?

I know, you people will come up with a solution.

With regards
Moses

Is the number [(44+\sqrt{1996})^{100}] odd or even?

I am confused while looking at it, help me to approach the problem to get the answer.

With regards
Moses