Calculus

30

Let y = 5x

Then think y = 5x^(1)

Differentioation at its most simplistic is to move the exponential to be a coefficient. Then taking the original expoential subtract '1' from it , and use the answer as the new expoential .

Algebraically

y = Ax^(n)

dy/dx = Anx^(n-1)

So for the above example

y = 5x^(1)

dy/dx = 5(1)x^(1-1)

dy/dx = 5(1)x^(0)

Now any value to the power of '0' equa; '1'.

Hence

dy/dx = 5(1)(1)

dy/dx = 5 The answer.

Undefined: You cannot divide by zero

y = x^(1/2) (NB power of '1/2' mean the 'square root'.

Hence

dy/dx = (1/2)x^(-1/2)

or

dy/dx = 1/ [2x^(1/2)]

Remember SecX = 1/CosX

Substitute

SinX X 1 /CosX =

SinX / CosX =

TanX

A 9-sided polygon, is named 'Nonagon'.

The number of diagonals are '9'

From any one node, to the centre of the opposite side.

Since there are 9 nodes and 9 lines, then there will be 9 diagonals.

1

y + 1 = 0

y = -1

So it would be a straight line, parallel with the x-axis at y = -1.

A Straight line !!!!

6x + 2y = 8

Algebriacally rearrange

2y = -6x + 8

y = -3x + 4

It is now in the straight line form of y = mx + c ,

The gradient'slope is '-3' and the y-intercept is '+4'.

x^(2) + y^(2) = 36 = 6^(2)

The graph is a circle of radius '6' , centred on the origin (0,0).

CosX = Sin2x

Using Trog. Identityt

CosX = 2SinXCosX

CosX cancels down to '1'

Hence

CosX/CosX = 2 SinX

1 = 2SinX

SinX = 1/2 = 0.5

SinX = 0.5

X = Sin^(-1) 0,5

X = 30 degrees = pi/6 radians

Cos (x) = -Sin(x)

1 = -Sin(x) / Cos (x)

1 = -Tan(x)

Tan(x) = -1

x = Tan^-1(-1(

x = -45 degrees = - pi /4 , 3pi/4, 5pi/4 ....

If you mean y = Sin(pi(x))

Then

Use the chain rule

dy/dx = dy/du X du/dx

Let

pi(x) = u

y = Sin (u)

dy/du = Cos(u)

u = pi(x)

du/dx = pi

Combining

dy/dx = pi Cos(u) = piCos (pi(x)). The answer!!!!!

Oh, isn't pi just a delightful number? Let's paint a picture with its first 35 digits: 3.1415926535897932384626433832795028. Just like adding happy little trees to a landscape, each digit of pi adds to the beauty and mystery of mathematics. Keep exploring and discovering, my friend.

974 x 7 = 6818

'x^(2)' looks like a bowl on a graph.

'-x^(2)' looks like an upturned bowl, or an umbrella.

Very simple: it is 1.6989700043 to be exact. You can test this because log50 means we assume the natural log (base 10), if you test 10 to the exponent of 1.6989700043 you should render 50 as your result :D

To convert a decimal into a fraction, write the decimal number over one like this: .52/1. Next, remove the decimal point and add as many zeroes to the bottom number as there were numbers after the decimal: .52/1 would now be 52/100. The last step is to simplify the fraction: 53/100 = 26/50 = 13/25. The fraction equivalent of .52 is 13/25.

y = Sin(x)

dy/dx = Cos(x)

10^3(8.75) would equal 10^26.25 which would equal: {| |- | 1.77828E+26 |}

x times 1 is x. Anything times 1 is still that same anything.

To graph the equation y - x + 3, we can first rearrange it into slope-intercept form, y = x - 3. This equation represents a line with a slope of 1 and a y-intercept of -3. To graph it, start by plotting the y-intercept at (0, -3), then use the slope to find another point, such as moving up 1 unit and to the right 1 unit. Connect these points with a straight line to complete the graph.

To calculate 10 percent of 6000, you first convert 10 percent to a decimal by dividing it by 100, which equals 0.10. Then, you multiply 0.10 by 6000 to find the answer. Therefore, 10 percent of 6000 is 600.

In Maths double sign symbols can be tabled as

• • = +
• • = -

• • = -
• • = +

NB If no symbol is given in front of a number, then read it as plus(+).

The word 'Mathemetics' comes from Classical Greece, and means 'to learn'.

Think of it as a puzzle , like a crossword puzlle, to be solved. However, there are a set of rules that you must follows in finding solutions, that are different from a crossword puzzle.

Board ganes, like Chess, or Snakes and Ladders have their own set of rules to follow in order to play the game fairly. Maths is the same, its just another different set of rules.