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C4 Differentiation help watch

1. 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.

2. (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.

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

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).
3. Moved to maths.
4. (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.

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

It is given that and we know that

(as )

5. Since when is differentiation of inverse trigonometric functions in c4?

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6. (Original post by drandy76)
Since when is differentiation of inverse trigonometric functions in c4?

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It's not
7. 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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8. For question 4 you should get (Y+xdy/dx)e^xy=0 then simplify from there

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9. (Original post by edothero)
It's not
Honestly thought it was MEI being weird with their spec again

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