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

=Newton Derivative of Polynomial Functions=

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

=Leibniz Derivative of Polynomial Functions=

1. The sum rule ${d(f+g) \over dx}={df \over dx}+{dg \over dx}$
2. The Difference Rule ${d(f-g) \over dx}={df \over dx}-{dg \over dx}$
3. The Product Rule ${d(fg) \over dx}'=f{dg \over dx}+g{df \over dx}$
4. The Quotient Rule ${d({f \over g}) \over dx}={g{df \over dx}-f{dg \over dx} \over g^{2}}$

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

1. NewtonChain rule $[f(g(x))]'=f'(g(x))*g'(x)$
2. LeibnizChain rule ${\frac {df(g(x))}{dx}}={{df(g)} \over dg}{dg \over dx}$

Derivatives of Logarithmic and Exponential Functions

1. Natural log of x$(lnx)'={1 \over x}$
2. log $(log_{a}x)'=({ln_{x} \over ln_{a}})'={1 \over ln_{a}}(lnx)'=$