Basic Calculus Flashcards
d/dx (sin 5x)
5 cos 5x
d/dx (tan 9x)
9 sec^2 (9x)
d/dx (cot 7x)
-7 csc^2 (7x)
d/dx (csc x^2)
-2x csc(x^2) cot(x^2)
Quotient Rule
lo d’hi - hi d’lo/ (lo)^2
Product Rule
1st d’2nd + 2nd d’1st
d/dx (cos u)
-sin u du/dx
d/dx (sin u)
cos u du/dx
d/dx (tan u)
sec^2 u du/dx
d/dx (cot u)
-csc^2 u du/dx
d/dx (sec u)
sec u tan u du/dx
If f(x) = c where c is a constant
then f’(x) = 0
Constant Rule
If f(x) = x, then f’(x) = 1
Identity Rule
If f(x) = x^n, then f’(x) = nx^n-1
Power Rule
If f(x) = Cx^n, then f’(x) = Cnx^n-1
Constant Multiple Rule
If f(x) = u(x) +/- v(x)
then f’(x) = u’(x) +/- v’(x)
Sum and Difference Rule
If f(x) = u(x) • v(x)
then f’(x) = u(x) - v’(x) + v(x) - u’(x)
Product Rule
If f(x) = u(x)/ v(x)
then f’(x) = v(x) - u’(x) - u(v) • v’(x)
/ [u(x)]^2
Quotient Rule
If f(x) = [u(x)]^n
then f’(x) = n [u(x)] ^ n-1 [u’(x)]
Chain Rule
e^5x
5e^5x
d/dx (e^2x)
2e^2x
d/dx (e^cos 3x)
u = cos 3x
cos (5x^2)
u = 5x^2
du = 10x
sin (3x^2)
u = 3x^2
du = 6x