Differentiation Flashcards
1
Q
A turning point is
A
where the gradient of a function changes sign in a continuous region of the graph
2
Q
+ve second derivative
A
minimum
3
Q
-ve second derivative
A
maximum
4
Q
second derivative = 0
A
point of inflection
5
Q
d/dx e^x
A
d/dx e^x = e^x
6
Q
d/dx e^kx
A
d/dx e^kx = e^kx
7
Q
d/dx e^(ax + b)
A
d/dx e^(ax + b) += ae^(ax + b)
8
Q
d/dx ln x
A
d/dx ln x = 1/x
9
Q
d/dx ln (ax + b)
A
d/dx ln (ax + b) = a/ (ax + b)
10
Q
d/dx ln ax
A
d/dx ln x = 1/ ax
11
Q
d/dx a^x
A
d/dx a^x = (ln a)a^x
12
Q
d/dx sin x
A
d/dx sin x = cos x
13
Q
d/dx cos x
A
d/dx cos x = -sin x
14
Q
d/dx sin kx
A
d/dx sin kx = k cos kx
15
Q
d/dx cos kx
A
d/dx cos x = -k sin kx
16
Q
Product Rule
A
dy/dx (uv) = u dv/dx + v du/dx
17
Q
Chain Rule
A
dy/dx ( f(g(x)) ) = dy/du x du/dx
18
Q
Quotient Rule
A
dy/dx (u/v) = ( v du/dx - u dv/dx) / v^2
19
Q
d/dx tan x
A
d/dx tan x = sec^2 x
