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Implicit Differentiation

Question:
http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/OCR-MEI/C3%20Differentiation%20-%20Implicit%201%20QP.pdf
Question 3
Starts as: Given that y=ln square root...

Answer:
http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/OCR-MEI/C3%20Differentiation%20-%20Implicit%201%20MS.pdf

My Question:
1) Why when differentiating is there is a 2 on top of the fractions before reaching the answer
2)Most importantly, how do I know that I need to differentiate implicitly?!
Could the quotient rule be used because there are two terms divided
Original post by esmeralda123
Question:
http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/OCR-MEI/C3%20Differentiation%20-%20Implicit%201%20QP.pdf
Question 3
Starts as: Given that y=ln square root...

Answer:
http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/OCR-MEI/C3%20Differentiation%20-%20Implicit%201%20MS.pdf

My Question:
1) Why when differentiating is there is a 2 on top of the fractions before reaching the answer
2)Most importantly, how do I know that I need to differentiate implicitly?!
Could the quotient rule be used because there are two terms divided


Ermm....

Firstly, you do not use implicit differentiation at all here. Secondly, you should know that ddxln⁡f(x)=f′(x)f(x)\dfrac{d}{dx} \ln f(x) = \dfrac{f'(x)}{f(x)} which is what is being used here.

I wouldn't advise quotient rule, clearly there is a much better way here due to properties of a logarithm.
Reply 2
Avatar for debbie394
debbie394
OP
11
Original post by RDKGames
Ermm....

Firstly, you do not use implicit differentiation at all here. Secondly, you should know that ddxln⁡f(x)=f′(x)f(x)\dfrac{d}{dx} \ln f(x) = \dfrac{f'(x)}{f(x)} which is what is being used here.

I wouldn't advise quotient rule, clearly there is a much better way here due to properties of a logarithm.


I don't understand
What type of differentiation is being used?
Original post by esmeralda123
I don't understand
What type of differentiation is being used?


Your usual differentiation from C1. Why do you think this is implicit differentiation?

The only part you differentiate implicitly is the LHS but that's trivial and you never even think about it even in C1; ddx(y)=dydx\dfrac{d}{dx}(y) = \dfrac{dy}{dx}
Reply 4
Avatar for debbie394
debbie394
OP
11
Original post by RDKGames
Your usual differentiation from C1. Why do you think this is implicit differentiation?

The only part you differentiate implicitly is the LHS but that's trivial and you never even think about it even in C1; ddx(y)=dydx\dfrac{d}{dx}(y) = \dfrac{dy}{dx}


it is because i am doing a set of questions on implicit differentiation.
do i use implicit when there is a mixture of x and ys on one side that I can't simply rearrange to one side??
Original post by esmeralda123
it is because i am doing a set of questions on implicit differentiation.
do i use implicit when there is a mixture of x and ys on one side that I can't simply rearrange to one side??


Well then I'm not sure what this question is doing there because it does not require implicit differentiation.

You use implicit differentiation when you differentiate an expression that contains different variables to what you're differentiating with respect to.

I.e. if you're differentiating with respect to xx then you would use it on any expression that contains other variables. Like xyxy or y3y^3 or (y+x)(y−x)(y+x)(\sqrt{y}-x), etc...

You wouldn't use it on expressions that are entirely made up of your variable, like ln⁡2x−12x+1\ln \sqrt{\dfrac{2x-1}{2x+1}}

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