Differentiation Flashcards Preview

Maths > Differentiation > Flashcards

Flashcards in Differentiation Deck (19):
1

A turning point is

where the gradient of a function changes sign in a continuous region of the graph

2

+ve second derivative

minimum

3

-ve second derivative

maximum

4

second derivative = 0

point of inflection

5

d/dx e^x

d/dx e^x = e^x

6

d/dx e^kx

d/dx e^kx = e^kx

7

d/dx e^(ax + b)

d/dx e^(ax + b) += ae^(ax + b)

8

d/dx ln x

d/dx ln x = 1/x

9

d/dx ln (ax + b)

d/dx ln (ax + b) = a/ (ax + b)

10

d/dx ln ax

d/dx ln x = 1/ ax

11

d/dx a^x

d/dx a^x = (ln a)a^x

12

d/dx sin x

d/dx sin x = cos x

13

d/dx cos x

d/dx cos x = -sin x

14

d/dx sin kx

d/dx sin kx = k cos kx

15

d/dx cos kx

d/dx cos x = -k sin kx

16

Product Rule

dy/dx (uv) = u dv/dx + v du/dx

17

Chain Rule

dy/dx ( f(g(x)) ) = dy/du x du/dx

18

Quotient Rule

dy/dx (u/v) = ( v du/dx - u dv/dx) / v^2

19

d/dx tan x

d/dx tan x = sec^2 x