How do you use implicit differentiation here? the answer should be (5x^4+4x^3y)/(6xy^2-4y^3) but I don't know how to get there
#x^4(x+y)=y^3(3x-y)#
2 Answers
That answer is not correct for this question. Whoever provided the answer made an error in the product rule. (Or they started with a different equation.)
Explanation:
The given equation is equivalent to
Differentiating with respect to
The correct answer (verified) is as follows:
Explanation:
Implicit differentiation is just an application of the chain rule. If
So we have
I would tackle this by first multiplying out:
We then differentiate everything wrt
We will now also need to apply the product rule
Now we can't differentiate functions of y wrt x but we can use the chain rule (and this is the implicit differentiation)
This subtle change allows s now to differentiate the non-explicit functions of y;
we can gather up the