Differentation more techniques Flashcards
What is the derative of f(x) = In(x)
1/x
What does the power law tells us for logs?




What yet dont we know how to differentatie?
In(x+k)
How can we use the change of base formula to find the derative of this function?


So what is the derative of this function again?



What is the derative of e^x? ( providing the base is an expoentital constant?
e^x
If we have a function where the base is not an expotential constant, when what do we do?

1) we take logs on both side ( when a doesnt equal 1)
2) then use power rule
3) we use that the our rules of logs ( logs

What functions can we not differentantiate without combination rules?

What are the 3 ways of combining functions other than what we saw in week 5?

What is the product rule?
f’g+fg’









What is the quotient rule?
The exact same line as product rule but divide by g(x) squared







When do we use the chain rule?
when differentiating a ‘function of a function’, like f(g(x)) in general.
What is the formula for the chain rule?


an alternative method is use power rule so
move the 2 down to get 2(x+1) times derative in the bracket which is 1


alternatively you could do:
use power rule to get 3(2x+1)^2 X the derative in the bracket 2 to get 6(2x+1)^2



Why couldnt we differentiate these functions previously??

because they were a funciton of a function, but now we can using the chain rule.
Differentatite using the chain rule these functions?

alternative for e^kx
i know that quickly i can got e^kx X the deraitve of the power which is k as k is a constant.
same for the last function, i can do these quickly

Differentatie this, this is a rule i need to learn


How would i find the derative of this difficult function?

I would use the product rule but within using product rule i have to use chain rule


We are going to use the product rule but the chain rule within

Whats the derative of 2e^x?
2e^x

f(g) = 3/(this means sqaure root g) =gx^1/3
f’(g) = 1/3g^-1/3
g(x) = 2x-1
g’(x) = 2
f’(g) x g’(x) = 2/3(2x-1)^2/3
How can we solve this using power rules instead of chain rule?

- 1(x^4+3)^-2
- 1(x^4+3)^-2 X 4x^3
- 4x^3(x^4+3)^-2
then turn this into a fraction easy

TBA



use chain rule and you should get 1


VERY HARD
1) Y = x^x
2) Take the natural log of both sides
InY = Inx^x( we can take expotent and move to the front)
InY = xInx
3) differentiate both sisdes with respect to x
1/y x dy/dx = ( On the RHS we use product rule) ( 1 In(x) + x times 1/x )
next step mutlple both sides by y


