INTRO

hi freinds this is the place where u can find amaging facts about maths.

all differentiation

1. Constant Rule:

If y = k, then y' = 0

The Derivative of a Constant is 0

If ƒ(x) = k for some constant k, then ƒ'(x) = 0

2. Power Rule

If y = x", then y' = nxn-1

If ƒ is a differentiable function, and if ƒ(x) = x", then ƒ'(x) = nxn-1 for any real number n

3. Exponential Rule:

If y = ex, then y' = ex

4. Logarithm Rule:

If y = 1n|x|, then y' = 1/x

5. Constant Times a Function Rule:

If y = kƒ, then y' = kf '

6. Sum Rule

If y = ƒ g, then y' = ƒ' g'

7. Product Rule

If y = ƒg, then y' = ƒg' ƒ' g

If ƒ and g are differentiable functions such that y = ƒ(x)g(x), then y' = ƒ(x)g' ƒ' (x)g(x)

8. Difference Rule

If y = ƒ - g, then y' = ƒ' - g'

9. Quotient Rule

To remember this formula: Simply remember that b comes before t in the alphabet Thus, the bottom function times the derivative of the top minus the top times the derivative of the bottom, all divided by the bottom squared!

10. Chain Rule:

If y is a differentiable function of u and u is a differentiable function of x and

formulae derivative

MULTIPLY

You only need seconds if you use and automate the use of the binomic formulas:

(x-y)(x+y) = x² – y² and (x+y)² = x² + 2xy + y²

then, e.g. : 83 * 87 = (85-2)(85+2) = (80+5)² – 2² = (6400+800+25) – 4 = 7221

automated: take the square of the tens, add 10 time the tens, add 25, subtract the square of difference to the number with the ending five (i.e. 85-83=2), voila.

1. 83 * 87 = 6400 + 800 + 25 – 4 = 7221
2. 24 * 26 = 400 + 200 + 25 – 1 = 624
3. 72 * 78 = 4900 + 700 + 25 – 9 = 5616
4. 99 * 91 = 8100 + 900 + 25 – 16 = 9009
5. 65 * 65 = 3600 + 600 + 25 – 0 = 4225

The 11 Rule

You can directly write down the answer to any number multiplied by 11.

• Take for example the number 51236 X 11.
• First, write down the number with a zero in front of it.

  051236

  The zero is necessary so that the rules are simpler.

• Draw a line under the number.
• Bear with me on this one. It is simple if you work through it slowly. To do this, all you have to do this is "Add the neighbor". Look at the 6 in the "units" position of the number. Since there is no number to the right of it, you can't add to its "neighbor" so just write down 6 below the 6 in the units col.
• For the "tens" place, add the 3 to the its "neighbor" (the 6). Write the answer: 9 below the 3.
• For the "hundreds" place, add the 2 to the its "neighbor" (the 3). Write the answer: 5 below the 2.
• For the "thousands" place, add the 1 to the its "neighbor" (the 2). Write the answer: 3 below the 1.
• For the "ten-thousands" place, add the 5 to the its "neighbor" (the 1). Write the answer: 6 below the 5.
• For the "hundred-thousands" place, add the 0 to the its "neighbor" (the 5). Write the answer: 5 below the 0.
  That's it ... 11 X 051236 = 563596

Multiply By 5

To quickly multiply by 5, divide the number in two and then multiply it by 10. Often this can be done quickly in your head.

Multiply By 4

To quickly multiply by four, double the number and then double it again.
Often this can be done in your head.