[adellie]

I was going through the C4 differentiation chapter for revision. I found the implicit differentiation questions really hard and am currently stuck on this question:

Ex 4B

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

1. (g)

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

... My solution was to do ....

[4(x-y)^3 * 1 * dy/dx)] = 1 + dy/dx + 5
[4(x-y)^3 * dy/dx] - dy/dx = 1 + 5
dy/dx[4(x-y)^3 - 1] = 1 + 5

dy/dx = (1 + 5)/(4(x-y)^3 - 1)

... but the answer should be: [4(x-y)^3- 1]/[1 + 4(x-y)^3]

Thanks!

[ghostwalker]

Two things:

a) The derivative of "5" is zero; it's just a constant.

b) To differentiate (x-y)^4, try a substitution, and then use the chain rule. Let z=x-y in this case.

[G.J.Speight]

Your differentiation is wrong. The first line should be:



Can you get it from here?

[adellie]

Originally Posted by G.J.Speight

Your differentiation is wrong. The first line should be:



Can you get it from here?

Thanks, I can now see you you differentiated the first bit. However, I can not think how i could multiply out "4(x-y)^3(1-dy/dx)" ... I'm having a mind blank!

[G.J.Speight]

Keep the part together, so .

[adellie]

Originally Posted by G.J.Speight

Keep the part together, so .

Thanks, I got the answer!

[G.J.Speight]

Great - thanks for the rep!