Differentiation Flashcards
1
Q
What is the definition of differentiation?
A
lim h->0 f(x+h)-f(x)/h
2
Q
[f(x)+g(x)]’ =…
A
f’(x)+g’(x)
3
Q
[cf(x)]’ =… where c is a constant
A
cf’(x)
4
Q
What is the product rule?
A
[f(x)g(x)]’ = f’(x)g(x)+f(x)g’(x)
5
Q
What is the quotient rule?
A
[f(x)/g(x)]’ = f’(x)g(x)’f(x)g’(x)/[g(x)]^2
6
Q
What is the chain rule
A
dy/dx = dy/du x du/dx
7
Q
f’(x) =
A
nx^n-1
8
Q
Derivative of sinx
A
cosx
9
Q
Derivative of cosx
A
-sinx
10
Q
Derivative of tanx
A
1/cos^2x
11
Q
Derivative of cotx
A
1/sin^2x
12
Q
Derivative of e^x
A
e^x
13
Q
Derivative of a^x
A
a^xlna
14
Q
Derivative of sin^-1x
A
1/sqrt(1-x^2)
15
Q
Derivative of cos^-1x
A
-1/sqrt(1-x^2)
