Chapter 3 Rules

Question 1

Power rule

Answer 1

d/dx(X^n) = nX^n-1

Question 2

Deriv of e^x

Answer 2

d/dx(e^x) = e^x

Question 3

Deriv of Constant Times function

Answer 3

d/dx(Cf(x)) = C * d/dx(f(x))

Question 4

Deriv of sum

Answer 4

d/dx(f(x)+g(x)) = d/dx(f(x) + d/dx(g(x)

Question 5

Deriv of difference

Answer 5

d/dx(f(x)-g(x)) = d/dx(f(x)) - d/dx(g(x))

Question 6

Product rule

Answer 6

d/dx(f(x) * g(x)) = f(x)g’(x) + f’(x)g(x)

or (UV)’=UV’ + U’V

Question 7

Quotient Rule

Answer 7

d/dx(f(x)/g(x)) = (g(x)f’(x) - g’(x)f(x))/g(x)^2

or (U/V)’ = (VU’ - U’V)/V^2

Question 8

Chain rule

Answer 8

d/dx((f*g) * x) =f’ (g(x)) * g’(x)

or (f(u))’= f’(u) * u’

Question 9

Generalized Power rule

Answer 9

d/dx([g(x)]^n) = n[g(x)]^n-1 * g(x)