Calculus

y = cos x
y'=?

y' = -sin x
y = sin x
y'=?

y' = cos x
y = tan x
y' =

y'=sec² x
y = cot x
y' = ?

y'=-csc²x
y = sec x
y'=?

y'=sec x * tan x
y = csc x
y'=

y'= csc x * cot x
Power Chain Rule
Given y = (f(x))ⁿ
y'=

y' = n (f(x))^n-1*f '(x)
Chain Rule
Given y = f(g(x))
y'= ?

y'= f '(g(x))*g'(x)
Exponential Functions
Given y = a^x
y'=?

y' = a^x * ln a
Implicit Differentation
- 1) Differentiate both sides w/respect to 'x'
- 2) Treat 'y' as function of 'x' and multiply 'y' by dy/dx
- 3) Collect all dy/dx on one side and solve for dy/dx
Normal/Perpendicular

take negative inverse of slope
Inverse Functions
- 1) Solve for 'x' in terms of 'y'
- 2) Swap domain (x) and range (y)
Derivitive of Inverse Function
y = f(x)
y'=?

y'= 1/f ' (x)
ln (a*b) = ?

ln a + ln b
ln (a/b) = ?

ln a - ln b
ln A^c= ?

C ln A
log_aa=?

1
a^log_ax=?

x
y = ln (f(x))
y' = ?

f ' (x) / f(x)
Trig Review
- sin 2x= 2sin x cos x
- cos2x=cos²x-sin²x
- sin(a+b) = sin a cos b + cos a sin b
- cos(a+b) = cos a cos b - sin a sin b

Author

ashleystewart

42254

Card Set

Calculus

Description

Calculus Exam #2

Updated

2010-10-15T00:28:55Z

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