Calculus

30

In general, if you're taking the derivative with respect to X, then you take the current power of X, multiply the given quantity by that number and then subtract one from the current power. In this case, that's an overcomplicated way of describing what happens but here's the process: 5x is more fully 5*x^1 So you take the power (1) and multiply it it by the given quantity. This gives you 1*5*x^1 Now you subtract one from the current power giving you 1*5*x^0 which equals 5. So the answer is simply 5 in this case. But what if you were trying to find the derivative of 4x^7? In this case, you would multiply the quantity by 7 (giving you 7*4*x^7) and subtract 1 from the current power giving you a final answer of 28*x^6. This also works for negative powers and square roots. The derivative of sqrt(x) can be found by recognizing that this is equal to x^(1/2). So you multiply everything by 1/2 and subtract one from the power and get 1/2 * x^(-1/2) which equals 1/2 * 1/sqrt(x) = 1/(2*sqrt(x))

Undefined: You cannot divide by zero

y = square root of x

y = x(1/2)

y' = (1/2)x(1/2 - 1)

y' = (1/2)x(-1/2)

y' = (1/2)(square root of x)

sinx*secx ( secx= 1/cos )

sinx*(1/cosx)

sinx/cosx=tanx

tanx=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

Y^2 = 36 - X^2

Y = (+/-)sqrt(36 - X^2)

A circle. X = (+/-) 6

Y = (+/-) 6

Cos(x) = Sin(2x)

Using angle-addition, we have Sin(a+b) = Sin(a)Cos(b) + Sin(b)Cos(a). From that, we see Sin(2x) = Sin(x)Cos(x)+Sin(x)Cos(x) = 2Sin(x)Cos(x)

Cos(x) = 2Sin(x)Cos(x)

If Cos(x) = 0, then the two sides are equal. This occurs at x= Pi/2 + nPi, where n is an integer and Pi is approximately 3.14.

If Cos(x) doesn't equal 0, then we can divide it out. Then,

1 = 2 Sin(x) , or

1/2 = Sin(x)

This occurs when x = Pi/6 or 5Pi/6, plus or minus any multiples of 2 Pi.

The derivative of cos(x) equals -sin(x); therefore, the anti-derivative of -sin(x) equals cos(x).

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

honestly,

a reaaallly happy smile :)

y=x^2

-has a turning point at (0,0)

-the range is R+ or [0, infinity)

-the domain is R or (-infinity, infinity)

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 |}

I suggest that you:* Solve the equation for variable "y".

* Make a table of values, by calculating the value of "y" for different values of "x".

* Plot the points

* Join them by lines

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.

A minus plus a minus will give a sum with a minus also.

As with anything, some people find math harder to learn that others. It may be that math is not one of your strongest areas, and some of the concepts are harder for you to grasp.

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Math isn't hard. Some people just aren't interested and won't work at it. Math is like sports. To be good you have to practice.

I presume that you mean 5x + 3y + 20 = 0 and 2x - y - 14 = 0.

First put the formulae in the form y = mx + c.

3y = -5x -20

y = -5/3 x -20/3

and

y = -2x + 14

Substitute the second formula into the first

-2x - 14 = -5/3 x -20/3

-6x - 42 = -5x - 20

-42 = x - 20

x = -22

Substitute into equation

y = -2x + 14

y = -2 x -22 + 14

y = 44 + 14

y = 58

Therefore the two lines meet at point (-22, 58).