2. POWER RULE
Derivative of (xn)is found by:
•
n ∙ xn-1
•
Multiply (x) by the exponent (n) then subtract 1 from
•
the original exponent (n).
Example: 1. if f(x) is x3 find f’(x).
•
•3 ∙ x3-1
•3x2 is the derivative.
3. PRODUCT RULE
If they ask you to find the derivative of a problem
•
where you need to multiply (example: (x3) (x2+2))
then you use the product rule:
y = u・v
•
• y’ = u・v’ + v・u’
y= (x3)(x2+2) u= x3
•
y’= (x3)(2x)+ (x2+2)(3x2) v= (x2+2)
•
u’= 3x2
v’=2x
4. TRIGONOMETRIC DERIVATIVES
For trig functions you do not use the power
•
rule, instead they each have their own
derivative.
y y’
•
sin x cos x
•
cos x -sin x
•
sec2x
tan x
•
-csc2x
cot x
•
sec x sec x tan x
•
csc x -csc x cot x
•
5. CHAIN RULE
You use chain rule when there is a problem usually
•
inside a parenthesis (then raised to a power), or
under a radical or in the denominator. You
substitute this with the letter u. so we solve the
derivative for u and later replace it for the original
function.
For example: 1. y= (x2+2)2 u=
•
x2+2
y= u2 du= 2x
y’= 2u ∙ du
y’= 2(x2+2) ∙ 2x
y’= 4x(x2+2)
6. DERIVATIVE OF EX
y= ex
y’= ex ∙ du
Example: y= e2x+1
y’= e2x+1 ∙ 2
y’= 2e2x+1
