Derivatives

1. Quotient Rule

1.1. f(x)=g(x)/h(x)

1.1.1. f'(x)=[g'(x)h(x)-g(x)h'(x)]/{[h(x)]^2}

2. Product Rule

2.1. f(x)=g(x)h(x)

2.1.1. f'(x)=g'(x)h(x)+g(x)h(x)

3. Trig Functions

3.1. f(x)=sin(x)

3.1.1. f'(x)=cos(x)

3.2. f(x)=cos(x)

3.2.1. f'(x)=-sin(x)

3.3. f(x)=tanx

3.3.1. f'(x)=sec^2(x)

4. Derivatives can be attributed to the work of Isaac Newton and Gottfried Leibniz.

4.1. Isaac Newton

4.2. Gottfried Leibniz

5. Power Rule

5.1. f(x)=x^n

5.1.1. f(x)'=nx^n-1

6. Practice Problems: Find the derivatives to these functions.

6.1. 1) f(x)=3x^2

6.2. 2) f(x)=4x^3+2x^2+2x+5

6.3. 3) f(x)=(3x+4)^2

6.4. 4) f(x)=(6x+2)(3x+1)

6.5. 5) f(x)=(4x^2)/(3x)

6.6. 6) f(x)=sin(x)cos(x)

7. Chain Rule

7.1. f(x)=g(h(x))

7.1.1. f'(x)=g'(h(x))h'(x)