Calculus

Calculus

This is a course that Henry and Ben are studying during 2021.

Differentiation

Power Rule

$(x^{n})'=n*x^{n-1}$

Derivative of Polynomial Functions

1. The sum Rule 1$(f+g)'=f'+g'$
2. The sum Rule 2Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {d(f+g)} \over {d x} ={d(f)} \over {d x} + {d(g)} \over {d x}}

1. The Difference Rule $(f-g)'=f'-g'$
2. The Product Rule $(f*g)'=f*g'+g*f'$
3. The Quotient Rule $({f \over g})'={(gf'-fg') \over g^{2}}$

Derivative of Trigonometric Functions

1. $(sinx)'=cos(x)$
2. $(cosx)'=-sin(x)$
3. $(tanx)'=sec^{2}(x)$
4. $(cotx)'=-csc^{2}(x)$
5. $(cscx)'=-csc(x)cot(x)$
6. $(secx)'=sec(x)tan(x)$

Chain Rule

$[f(g(x))]'=f'(g(x))*g'(x)$

${\frac {df(g(x))}{dx}}={{df(g)} \over dg}{dg \over dx}$