example solving: 7-5(x-4)<-8

7-5(x-4)<-8 subtract 7 from both sides

-5(x-4)<-15 add 5(x-4) to both sides and add 15 to both sides (or it's easier to remember that if you multiple -1 to both sides you switch the sign)

5(x-4)>15 divide 5 from both sides

x-4>3 add 4 to both sides

There are 3 symbols that represent the derivative of a function

1) f'(x) pronounciation - f prime of x

2) y' pronounciation - y prime

3) dy/dx (leibniz notation) pronounciation - dee y by dee x

If h(x) = f(x) + g(x)

Then h'(x) = f'(x) + g'(x)

 Proof:

The objective for calculus is to find the instant rate of change (aka derivative), or the slope of tangent. To find the instant rate of change, we need 1st principle.

First of all, to find the slope of anything, the equation is