chapter 2: derivatives Flashcards
so much suffering
1
Q
d/dx (csc x)
A
- cscx cotx
2
Q
d/dx (sec x)
A
secx*tanx
3
Q
d/dx (cot x)
A
-csc²x
4
Q
if f(x) = ln(u), then f’(x) = …
A
(1 / u) * u’
5
Q
if f(x) = eᵘ, then f’(x) = …
A
(eᵘ)(u’)
6
Q
Logarithmic differentiation
A
- Necessary when base and exponent are both functions of x (ie, (cosx)^x)
1) Take natural log of both sides of the equation
2) Differentiate as usual
3) Solve for y’ or dy/dx (depending on notation)
7
Q
if f(x) = aᵘ (a is a non-e base), then f’(x) =
A
(aᵘ )(u’)(lna)
8
Q
if f(x) = logₐu, then f’(x) =
A
(1 / lna) (1 / u) u’
9
Q
Implicitly differentiable function
A
When a function cannot be (easily / at all) solved for y
10
Q
Monotonic
A
(Of a function) only increasing or only decreasing on an interval
11
Q
d/dx (arcsin u)
A
(u’) / (√1 - u²)
12
Q
d/dx (arccos u)
A
- (u’) / (√1 - u²)
13
Q
d/dx (arcsec u)
A
(u’) / [|u|(√u² - 1)]
14
Q
d/dx (arccsc u)
A
- (u’) / [|u|(√u² - 1)]
15
Q
d/dx (arctan u)
A
(u’) / (1 + u^2)
