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C4 Differentiation help

Hi, I have many questions about implicit differentiation (which we didn't learn how to do in class I guess):

1. Given that x = cos(y), find dy/dx in terms of x, using the fact y = cos^-1x

2. Given that x = tan(y), find dy/dx in terms of x, using the fact y = tan^-1x

3. Given y = x^x^2, find dy/dx in terms of x.

4. Find dy/dx in terms of x and y for the equation: e^xy = 2 (answer is = y/x, but I'm getting -e^x/e^y)

For Q1-2 I can find dy/dx in terms of x and y, but I find dy/dx in terms of x by using the facts.

Thanks in advance.
Original post by TheKevinFang
Hi, I have many questions about implicit differentiation (which we didn't learn how to do in class I guess):

1. Given that x = cos(y), find dy/dx in terms of x, using the fact y = cos^-1x

2. Given that x = tan(y), find dy/dx in terms of x, using the fact y = tan^-1x

3. Given y = x^x^2, find dy/dx in terms of x.

4. Find dy/dx in terms of x and y for the equation: e^xy = 2 (answer is = y/x, but I'm getting -e^x/e^y)

For Q1-2 I can find dy/dx in terms of x and y, but I find dy/dx in terms of x by using the facts.

Thanks in advance.


This belongs in the Maths forum :h: I've asked for this thread to be moved there. :borat:

It's not quite clear what you mean for Q1/2 - please post working if possible.

What have you tried for Q3/4? (You've got an answer for 4 but we can't see where you're going wrong or why).
Reply 2
Moved to maths.
Original post by TheKevinFang
Hi, I have many questions about implicit differentiation (which we didn't learn how to do in class I guess):

1. Given that x = cos(y), find dy/dx in terms of x, using the fact y = cos^-1x

2. Given that x = tan(y), find dy/dx in terms of x, using the fact y = tan^-1x

3. Given y = x^x^2, find dy/dx in terms of x.

4. Find dy/dx in terms of x and y for the equation: e^xy = 2 (answer is = y/x, but I'm getting -e^x/e^y)

For Q1-2 I can find dy/dx in terms of x and y, but I find dy/dx in terms of x by using the facts.

Thanks in advance.


Ill do Q1 for you and see if you spot how I'm doing it, I can explain if needed. Then you can try the rest

x=cosyx = cosy

dxdy=siny\dfrac{dx}{dy} = -siny

dydx=1siny\therefore \dfrac{dy}{dx} = -\dfrac{1}{siny}

It is given that x=cosyx=cosy and we know that cos2y+sin2y=1cos^{2}y+sin^{2}y=1

sin2y=1cos2y sin^{2}y = 1-cos^{2}y

siny=1cos2y\therefore siny = \sqrt{1-cos^{2}y}

siny=1x2siny = \sqrt{1-x^{2}} (as x=cosyx=cosy)

dydx=11x2\therefore \dfrac{dy}{dx} = -\dfrac{1}{\sqrt{1-x^{2}}}
Since when is differentiation of inverse trigonometric functions in c4?


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Original post by drandy76
Since when is differentiation of inverse trigonometric functions in c4?


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It's not
Using implicit differentiation :
X=cosy
1=-siny dy/dx
Dy/dx = -1/siny
Siny =(1-cos^2x)^1/2
X^2=cos^2x
Dy/dx =-1/(1-x^2)^1/2


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For question 4 you should get (Y+xdy/dx)e^xy=0 then simplify from there




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(edited 8 years ago)
Original post by edothero
It's not


Honestly thought it was MEI being weird with their spec again


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