Important rules to remember for chapter 3 Flashcards
1
Q
Derivate of e^x is
A
e^x
2
Q
(fg) prime is
A
fg^’ + gf^’
3
Q
f/g prime si
A
gf^’ - fg^’/g^2
4
Q
Sometimes it is easier to do what to a quotient rule?
A
REWRITE
5
Q
Derivative of sinx
A
cosx
6
Q
Derivative of cosx
A
-sinx
7
Q
Derivative of tanx
A
sec^2x
8
Q
Derivative of cscx
A
-cscx * cotx
9
Q
Derivative of secx
A
secx * tanx
10
Q
Derivative of cotx
A
-csc^2x
11
Q
What is the chain rule
A
f^’(g(x)) * g^’(x)
12
Q
Derivative of logbx
A
1/x ln b
13
Q
Derivative of lnx
A
1/x
14
Q
What are the steps of Logarithmic Differentiation?
A
- Take natural logarithms of both sides of an equation y =f(x) and use the Laws of Logarithms to simplify
- Differentiate implicitly with respect to x
- Solve the resulting equation for y^’
15
Q
Growth and Decay Equation
A
y(t) = y(0)e^kt
16
Q
Radioactive Decay
A
m(t) = m0e^kt
17
Q
Linear Approximation
A
L(x) = f(a) + f’(a)(x-a)
18
Q
Differential Equation
A
dy = f’(x)dx
19
Q
Triangle Y Equation
A
f(x + <>x) - f(x)
20
Q
sinh x
A
e^x - e^x-x / 2
