Derivative Rules Flashcards
1
Q
Sum Rule: d/dx [f(x) + g(x)] = ?
A
d/dx [f(x)] + d/dx [g(x)]
2
Q
Difference Rule: d/dx [f(x) - g(x)] = ?
A
d/dx [f(x)] - d/dx [g(x)]
3
Q
Constant Multiple Rule:
d/dx [c ⋅ f(x)] = ?
A
c ⋅ d/dx [f(x)]
4
Q
Power Rule:
d/dx (x^n) = ?
A
n ⋅ x^(n - 1)
5
Q
What is the derivative of y = mx + b ?
A
The slope, m
6
Q
What is d/dx (2x^4) ?
A
8x^3
7
Q
What is d/dx (6x) ?
A
6
8
Q
Constant rule: d/dx (c) = ?
A
0
9
Q
What is d/dx (3x^2 + 5) ?
A
d/dx (3x^2) + d/dx (5)
6x + 0
6x
10
Q
Product rule: d/dx (fg) = ?
A
g ⋅ d/dx(f) + f ⋅ d/dx(g)
11
Q
d/dx (e^x) = ?
A
e^x
12
Q
d/dx (a^x) = ?
A
ln(a) ⋅ a^x
13
Q
Quotient rule: d/dx(f/g) = ?
A
(f ⋅ g’ - g ⋅ f’)/g^2
14
Q
Chain rule: d/dx (f ∘ g) = ?
A
(f’ ∘ g) ⋅ g’
