Differentiation Flashcards
(12 cards)
1
Q
How would you prove that sinx differentiates to cosx ?
A
- expand using the double angle formulae
- separate the fraction
- factorise sinx
- use small angle approximation
- cancel h
- make h > 0
2
Q
What does sinx differentiate to ?
A
Cos x
3
Q
What does cos x differentiate to ?
A
-sinx
4
Q
What function differentiates to itself ?
A
e^x
5
Q
What does e ^kx differentiate to ?
A
Ke^kx
6
Q
What does a^x differentiate to ?
A
Ln a * a^x
7
Q
What does a^kx differentiate to ?
A
K ln a * a ^kx
8
Q
What does lnx differentiate to ?
A
1/ x
9
Q
What does ln(kx) differentiate to ?
A
1/x
10
Q
What does 5ln x differentiate to ?
A
5/x
11
Q
What does tan x differentiate to ?
A
Sec ^2 x
12
Q
What does sec x differentiate to ?
A
Sec x tan x
