Differentiation Flashcards
Constant Rule d(c)
0
Sum/Difference Rule d(f +/- g)
(f ‘) +/- (g ‘)
Product Rule d(fg)
f(g ‘) + g(f ‘)
Quotient Rule d(f/g)
[g(f ‘) - f(g ‘)]/ g^2
Constant Multiple Rule d(cf)
c(f ‘)
Power Rule d(x^n)/d(x)
nx^(n-1)/ 1
d(sin(x))
cos(x)
d(cos(x))
-sin(x)
d(tan(x))
sec^2(x)
d(sec(x))
sec(x)tan(x)
d(csc(x))
-csc(x)cot(x)
d(cot(x))
-csc^2(x)
Chain Rule d[f(u)]
f ‘(u) x u ‘ or f ‘(g(x)) x g ‘(x)
What is similar to Chain Rule?
Order of Operations
General Power Rule d[u^n]
nu^(n-1) x u ‘
What is a Derivative?
Slope or Rate of Change
Physics
Veloc= Posit ‘, Accel=Veloc ‘, Accel=Posit ‘’
Velocity
(Position(x)-Position(y))/(Time(x)-Time(y))
Acceleration
(Velocity(x)-Velocity(y))/(Time(x)-Time(y))
Limit Definition
[f(x+h)-f(x)]/h
If f is differentiable at x=c
f is continuous at x=c
No Derivative #1
Discontinuity
No Derivative #2
Absolute Value or Sharp Turn (or “Will” function that is W-shaped)
No Derivative #3
Square Root
