Week 1 Flashcards
1
Q
What is the product rule?
A
d/d(x) [f(x)g(x)] = fg’ + gf’
2
Q
What is the quotient rule?
A
d/d(x) [f(x)/g(x)] = (gf’ - fg’)/g^2 or [lowd(high) - highd(low)] / (low sq’d)
3
Q
What is the derivative of e^x?
A
e^x
4
Q
What is the chain rule?
A
F(x) = f(g(x)) and F'(x) = f'(g(x)) * g'(x) y = f(u) and u = g(x) --> dy/dx = (dy/du) * (du/dx)
5
Q
Rewrite b^x
A
(e^lnb)^x –> e^((lnb)*x)
6
Q
What is the derivative of b^x
A
lnb * b^x
7
Q
What is the derivative of sin?
A
cos
8
Q
Rewrite cos^2(x)
A
(cos(x))^2
9
Q
What’s the derivative of cos?
A
-sin
10
Q
What’s the derivative of 2^x?
A
ln2 * 2^x
11
Q
What’s the derivative of tanx?
A
sec^2 * x
12
Q
How do you tell if f(x) and g(x) are inverses of each other?
A
If f(g(x)) = x
13
Q
If f(x) and g(x) are inverses of each other, what is g’(x)?
A
1/[f’(g(x))]
14
Q
What is the inverse of y = e^x
A
y = lnx
15
Q
What is the derivative of lnx?
A
1/x
