# Calculus.txt

The flashcards below were created by user williams on FreezingBlue Flashcards.

1. y = cos x
y'=?
y' = -sin x
2. y = sin x
y'=?
y' = cos x
3. y = tan x
y' =
y'=sec2 x
4. y = cot x
y' = ?
y'=-csc2x
5. y = sec x
y'=?
y'=sec x * tan x
6. y = csc x
y'=
y'= csc x * cot x
7. Power Chain Rule
Given y = (f(x))n
y'=
y' = n (f(x))n-1*f '(x)
8. Chain Rule
Given y = f(g(x))
y'= ?
y'= f '(g(x))*g'(x)
9. Exponential Functions
Given y = ax
y'=?
y' = ax * ln a
10. 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
11. Normal/Perpendicular
take negative inverse of slope
12. Inverse Functions
• 1) Solve for 'x' in terms of 'y'
• 2) Swap domain (x) and range (y)
13. Derivitive of Inverse Function
y = f(x)
y'=?
y'= 1/f ' (x)
14. ln (a*b) = ?
ln a + ln b
15. ln (a/b) = ?
ln a - ln b
16. ln Ac= ?
C ln A
17. logaa=?
1
18. alogax=?
x
19. y = ln (f(x))
y' = ?
f ' (x) / f(x)
20. 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: williams ID: 52842 Card Set: Calculus.txt Updated: 2010-12-02 10:41:14 Tags: calculus Folders: Description: trig Show Answers: