Hi there, I'm having a hard time solving this particular 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
Now, the answer from the solutions manual is supposed to be
∂t/∂x = x^2 + y^2/4x^2y^3
∂t/∂y =y2 − 3x2/4xy4
Here's what I tried:
∂t/∂x = (2x - y^2)(4xy^3) - (x^2 - y^2)(4y^3)/ (4xy^3)^2
I couldn't come up with the right answer this way, I know I'm missing the chain rule here, according to the problem it has to be applied somewhere but I can't just figure out how. Can someone help me out with this?
Hi - cherry-picking here and two days late but...
Just in case a picture helps...
... If so, try the same for .
... is the chain rule for two inner functions, i.e...
As with...
... the ordinary chain rule, straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the (corresponding) dashed balloon expression which is (one of) the inner function(s) of the composite expression.
Similar example at http://www.mathhelpforum.com/math-he...tml#post374503. Have shaded here though the expressions that were held constant on the way down (whilst differentiating with respect to some other expression).
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