derivatives

Question 1

What is the derivative of y = e^x?

Answer 1

y’ = e^x Itself!

Question 2

What is the derivative of y = sinx?

Answer 2

y’ = cosx

Question 3

What is the derivative of y = cosx?

Answer 3

y’ = -sinx (Watch out, it’s negative!)

Question 4

What is the derivative of y = lnx?

Answer 4

y’ = 1/x

Question 5

What is the derivative of y = a(x^b) (Power Rule)

Answer 5

y’ = a(b)(x^(b-1)) Multiply the power and constant, then subtract one from the original power.

Question 6

Product Rule What is the derivative of y = (f)(g) where f and g are functions of x.

Answer 6

y’ = (f)(g’) + (g)(f’) The first function times the derivative of the second, plus the second funciton times the derivative of the first function.

Question 7

Quotient Rule What is the derivative of y = (f/g), where f and g are functions of x?

Answer 7

y’ = [(g)(f’) - (f)(g’)]/g^2 The bottom function times the derivative of the top, minus the top funciton times the derivative of the bottom function, then divide everything by the bottom function squared.

Question 8

Chain Rule What is the derivative of y = f(g(x))? This involves a composition of two functions, an outside function, f, and an inside function, g(x).

Answer 8

y’ = f’(g(x)) times g’(x) y’ = Do times DI The derivative of the outside function(evaluated with the inside function) times the derivative of the inside function.