Chapter 4

Product Rule:

If f(x) is a product of two functions, g(x) and h(x), then the derivative of f(x) = the derivative of the first function times the second function plus the derivative of the second function times the first function.

Let f = g times h. f´ = g´h + h´g

Quotient Rule:

f = (numerator function)/(denominator function), the quotient of two functions.

f´ = n´d – d´n

d²

Chain Rule:

If f(x) is a composite function such as sin(5x) then the derivative of sin(5x) equals cos(5x) times 5; the derivative of a composite function equals the derivative of the outside function in terms of its inside function times the derivative of the inside function. (if the inside function is not x then, that function is an outside function so another chain rule must be applied)

Ex: f = sin((5x)²)

f´= cos((5x)²) 2(5x)¹ 5

Derivatives of Trigonometric functions:

1) sin´x = cosx

2) tan´x = (secx)² = sec² x

3) sec´x = secxtanx

4) cos´x = -sinx

5) cot´x = -csc²x

6) csc´x = -cscxcotx