# 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

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#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