Derivatives Flashcards
1
Q
Power Rule
A
If f(x) = x^n, then f’(x) = n*x^(n-1).
2
Q
Product Rule
A
If f(x) = u(x) * v(x), then f’(x) = u’(x) * v(x) + u(x) * v’(x).
3
Q
Quotient Rule
A
If f(x) = u(x) / v(x), then f’(x) = (u’v - uv’) / v^2.
4
Q
Chain Rule
A
If f(g(x)) is a composite function, then the derivative is f’(g(x)) * g’(x).
5
Q
Constant Multiple Rule
A
If f(x) = c * g(x), then f’(x) = c * g’(x).
6
Q
Derivative of cos(x)
A
-sin(x).
7
Q
Derivative of sin(x)
A
cos(x)
8
Q
Derivative of sec(x)
A
sec(x)tan(x)
9
Q
Derivative of csc(x)
A
-cos(x)cot(x)
10
Q
Derivative of tan(x)
A
sec^2(x)
11
Q
Derivative of cot(x)
A
-csc^2(x)
12
Q
Derivative of ln(u)
A
u’/u
13
Q
Derivative of log a (u)
A
(1/ln(a)) * (u’/u)
14
Q
Derivative of e^u
A
e^u *u’
15
Q
Derivative of a^u
A
ln a * a^u * u’
16
Q
Horizontal tangent line
A
f ‘(x) = 0
17
Q
Vertical tangent line
A
f ‘(x) = und
