Question

What is calculus?

Answer 1

Look below

Explanation:

Calculus is sectioned off into 3 parts, differential calculus (calculus 1), integral calculus (calculus 2), and multi variable calculus (calculus 3).

calculus 1:
This deals with the limits (for ex. `lim_{x->0} 3x^2`) and the discontinuities of the limits from equations (mainly expressions) and graphs.
`lim_{x->0} cscx` does not exist.
graph{csc(x) [-10, 10, -5, 5]}

and it also deals with derivatives of simple and complex functions.

`d/dx 2x^2 = 4x`

derivative rules:

power rule:
the power rule is used by the formula `nx^{n-1}`

quotient rule
the quotient rule is used by the formula `\frac{f'g-g'x}{g^2}`
note: use quotient rule if there is a fraction.

product rule
`f'g+g'f`

the `d/dx x = 1` and the `d/dx n=0`, n being a constant

you can also use the definition of a limit

`lim_{x->0} \frac{f(x+h)+f(x)}{h}`

derivatives of trig functions

trig is used a lot, so as much as the derivatives.

`d/dxsin(x)=cos(x)` this goes on a loop back to `sin(x)`
`d/dxcos(x)=-sin(x)`
`d/dx-sin(x)=-cos(x)`
`d/dxtan(x)=sec^2(x)`
`d/dx(secx)=secx*tanx`
`d/dxcsc=-csc*cot`
`d/dxcot=-csc`

calculus 2

since my computer can handle me typing this much, ill talk about calculus 2 definite integrals here, and indefinite integrals and calculus 3 in the comments.

definite integrals are in the form `int_a^b f(x)dx`.