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Need help with multi-variable Chain Rule.
- Thread starter Treize
- Start date
D
Deleted member 4993
Guest
Treize said:Hi there, I need some help solving this problem:
"Use appropriate forms of the chain rule to find the derivatives"
Let t = u/v; u = X^2 - y^2, v = 4xy^3
Find ?t/?x and ?t/?y
?t/?x = ?t/?u * ?u/?x + ?t/?v * ?v/?x
and
?t/?y = ?t/?u * ?u/?y + ?t/?v * ?v/?y
Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
Ok, I have ?t/?x = ?t/?u*?u/?x + ?t/?v*?v/?x
?t/?x= (1/v)(2x - y^2) + (-u/v^2)(4y^3)
?t/?x= [(2x - y^2)/(4xy^3)] - [(4x^2y^3-4y^5)/(16x^2y^6)]
This is where I'm stuck, the answer for ?t/?x is supposed to be (x^2+y^2)/(4x^2y^3) but I can't seem to get there from what I did up there.
?t/?x= (1/v)(2x - y^2) + (-u/v^2)(4y^3)
?t/?x= [(2x - y^2)/(4xy^3)] - [(4x^2y^3-4y^5)/(16x^2y^6)]
This is where I'm stuck, the answer for ?t/?x is supposed to be (x^2+y^2)/(4x^2y^3) but I can't seem to get there from what I did up there.
D
Deleted member 4993
Guest
Treize said:Ok, I have ?t/?x = ?t/?u*?u/?x + ?t/?v*?v/?x
?t/?x= (1/v)(2x - y^2) + (-u/v^2)(4y^3)
?t/?x= [(2x - y^2)/(4xy^3)] - [(4x^2y^3-4y^5)/(16x^2y^6)]
This is where I'm stuck, the answer for ?t/?x is supposed to be (x^2+y^2)/(4x^2y^3) but I can't seem to get there from what I did up there.
Let t = u/v; u = X^2 - y^2, v = 4xy^3
?t/?u = 1/v ..........................?t/?v = =u/v[sup:1gz8xdzr]2[/sup:1gz8xdzr]
?u/?x = 2x ...........................?u/?y = -2y
?v/?x = 4y[sup:1gz8xdzr]3[/sup:1gz8xdzr] ...........................?v/?y = 12xy[sup:1gz8xdzr]2[/sup:1gz8xdzr]
Your calculation of ?u/?x was incorrect.
Try it again now.....