Reflection

MID TERM EXAMS ARE COMING UPPPP!!!!!!!!!!!!!!
REVIEW EVERYTHING!!!!!! WAAAAAAAAAAAAAAAAA

-A jump on a graph will NEVER have a limit
-An asymptote will SOMETIMES have a limit
-A removable will ALWAYS have a limit

Constant Rule: y=7 the constant rule says the derivative of any constant is zero, so the derivative is zero.

Power Rule: f(x)=x^6 move the 6 to the front and subtract one from the exponent and your derivative would be 6x^5

derivative of sin and cos...
If you have cos(x) then the derivative is sin(x). When you have sin(x) the derivative is -cos(x)

-Product Rule:
f(x)g(x) = f(x)g’(x) + g(x)f’(x)(copy 1st)(derivative 2nd) + (copy 2nd)(derivative 1st)

-Quotient Rule:
f(x)/g(x) = g(x)f’(x) – [f(x)g’(x)] / (g(x))^2(copy bottom)(derivative top) – [(copy top)(derivative bottom)] / (bottom)^2

Chain Rule:
Derivative of the outside (recopy inside) times the (derivative of the inside)

Implicit functions not solved for y and explicit functions means it is solved for y.

Rolle's Theorem Steps:
1.) Mak sure it is continuous
2.) If so make sure it is differentiable
3.) Make sure y - values match
4.) Take derivative equal; solve for x

Expand :
lnx^2y/10
=2 ln x + ln y - ln 10

Condense :
3 ln ( x + 2 ) - ln ( x - 1 )
= ln ( x + 2 ) ^3 / ( x - 1 )

Taking a Derivative :

d / dx ln u = 1 / u * d (u)
d / dx ln 2 x
=1 / 2x * 2
=1 / x