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Edexcel C4 - Exercise 4B - Question 1G (page 40 of the new textbook)

This question has confused me for the past hour or so, I simply can't get to the answer. Any help would be appreciated :wink:

Find and expression in terms of x and y for dy/dx, given that:

(x-y)^4=x+y+5

thanks!!!
:smile::smile:
Reply 1
Have you differentiated it implicitly?

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Reply 2
yes and i ended up with: 4(x-y)^3(1-dy/dx)=1+dy/dx have no clue what to do next!!! btw i got the left hand side by using chain rule.
Original post by harris12345
yes and i ended up with: 4(x-y)^3(1-dy/dx)=1+dy/dx have no clue what to do next!!! btw i got the left hand side by using chain rule.


Rearrange this to find dy/dx.
Reply 4
Original post by brittanna
Rearrange this to find dy/dx.


thats the part where im struggling. the question seems different to others in the same exercise.
Original post by harris12345
thats the part where im struggling. the question seems different to others in the same exercise.


So you have 4(xy)3(1dydx)=1+dy/dx4(x-y)^3(1-\frac{dy}{dx})=1+dy/dx

Then 4(xy)34(xy)3dydx=1+dydx.4(x-y)^3 - 4(x-y)^3\frac{dy}{dx} = 1 + \frac{dy}{dx}.

4(xy)31=dydx(1+4(xy)3)4(x-y)^3 - 1 = \frac{dy}{dx}\left(1+4(x-y)^3\right).

Can you see what to do from here? Does this all make sense?
(edited 9 years ago)
Reply 6
Original post by brittanna
So you have 4(xy)3(1dydx)=1+dy/dx4(x-y)^3(1-\frac{dy}{dx})=1+dy/dx

Then 4(xy)34(xy)3dydx=1+dydx.4(x-y)^3 - 4(x-y)^3\frac{dy}{dx} = 1 + \frac{dy}{dx}.

4(xy)31=dydx(1+4(xy)3)4(x-y)^3 - 1 = \frac{dy}{dx}\left(1+4(x-y)^3\right).

Can you see what to do from here? Does this all make sense?


how did u get the -4(x-y)^3dy/dx in the second step?
Original post by harris12345
how did u get the -4(x-y)^3dy/dx in the second step?


I multiplied out the bracket. a(bc)=abac.a(b-c) = ab - ac.

Just let a=4(xy)3,b=1,c=dydxa = 4(x-y)^3, b=1, c=\frac{dy}{dx}.
Reply 8
Original post by brittanna
I multiplied out the bracket. a(bc)=abac.a(b-c) = ab - ac.

Just let a=4(xy)3,b=1,c=dydxa = 4(x-y)^3, b=1, c=\frac{dy}{dx}.


aaah that all makes sense. I appreciate the help mate thanks for takin out ur time!!:smile:
thank you, really helpful

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