Differentation Flashcards
When is the chain rule used?
It is used when you have a function within brackets to the power of something and you have to differentiate it.
Differentiate y=(3x²+4x-1)⁵
u=3x²+4x-1 Y=u⁵
u’=6x+4 Y’=5u⁴
(6x+4)5u⁴
Sub U back in and expand.
When is the product rule used?
When you have to differentiate an equation which is made of two different parts multiplied together. Each part can be differentiated on its own.
What is the product rule?
dy/dx= vu’ + uv’
When is the quotient rule used?
It is used when you have to differentiate a function which is made of two different parts, one divided by the other. You have to be able to differentiate each part on its own.
When you are using the quotient rule, which part is U and which is V?
The one on top is U and the one on the bottom is V
What is the quotient rule?
(vu’ - uv’) ÷ v²
What is sin x differentiated?
cos x
What is cos x differentiated?
-sin x
What is tan x differentiated?
1÷cos²x. Should need to prove this, use the quotient rule and the knowledge tanx=sinx÷cosx
What is eᴷ differentiated?
eᴷ
What is 1n(x) differentiated?
1÷x
Differentiate (e^3x+1)
u=3x+1 y=e^u
u’=3 y’=e^u
dy/dx= 3e^3x+1
How would you differentiate 1n(1+x-x²)
First diff 1+x-x² to get 1-2x It is (1-2x)÷(1+x-x²)
What is the differential of 3sin x?
3 cos x
