Formulas Flashcards
D/dx (sin u)
= cos u du/dx
D/dx (cos u)
-sin u du/dx
D/dx (tan u)
Sec^2 u du/dx
D/dx (cot u)
= -csc^2u du/dx
D/dx (sec u)
Sec u tan u du/dx
D/dx (csc u)
- csc u cot u du/dx
D/dx ln u
(1/u)(du/dx)
D/du a^u
(A^u)(ln a)(dx /du)
D/dx loga(u)
1/(u * ln a) (du/dx)
X^n
E^nlnx - sub e, take derivative of exponent, then revert e back to original number and simplify
D/dx(sin-1u)
(1/sqrt(1-u^2))(du/dx)
Limit of inverse functions
Find value on unit circle
Finding normal line equations
Use implicit and plug in for x & y - slope is (-1/m)
Find a when solving for b. Then plug a into derivative of equation
Velocity
Derivative of position (s)
Acceleration
Derivative of velocity (v)
How long to reach highest point?
Velocity = 0 - solve for 0 in velocity equation
How long does it take object to reach half its height?
2 separate times - plug height into position formula and use quadratic to find both times.
How long is object aloft?
Find time for when position is o. Solve s for 0. When squared, one t = before it was thrown. The other is the answer.
