Unit 3 - More Derivatives Flashcards
1
Q
Chain Rule
A
f(g(x)) = f’(g(x))*g’(x)
2
Q
Chain Rule (notation)
A
dy/dx = dy/du*du/dx
3
Q
Finding dy/dx parametrically
A
dy/dx = (dy/dt) / (dx/dt)
4
Q
(f^-1)’(b) =
A
1/f’(a)
5
Q
Derivatives of inverse functions (definition)
A
If f is differentiable at every point on interval I and f’(x) is never zero on I, then f has an inverse and f^-1 is differentiable at every point on interval I
6
Q
d/dx(sin^-1x)
A
1/sqrt(1-x^2)
7
Q
d/dx(tan^-1x)
A
1/(1+x^2)
8
Q
d/dx(sec^-1x)
A
1/(|x|sqrt(x^2-1))
9
Q
d/dx(cos^-1x)
A
pi/2 - sin^-1(x)
10
Q
d/dx(cot^-1x)
A
pi/2 - tan^-1(x)
11
Q
d/dx(csc^-1x)
A
pi/2 - sec^-1(x)
12
Q
Calculator conversion -
d/dx(sec^-1x)
A
cos^-1(1/x)
13
Q
Calculator conversion -
d/dx(cot^-1x)
A
pi/2 - tan^-1(x)
14
Q
Calculator conversion -
d/dx(csc^-1x)
A
sin^-1(1/x)
15
Q
d/dx(e^x)
A
e^x
