# Thread: what will this d/dx y^3 be?

1. ## what will this d/dx y^3 be?

d/dx y^3 will equal to zero or 3y^2 ?

2. ## Re: what will this d/dx y^3 be?

If y is a function of x, then you also need to apply the chain rule to get:

$\displaystyle \frac{d}{dx}(y^3)=3y^2\frac{dy}{dx}$

3. ## Re: what will this d/dx y^3 be?

this kind of confuses me. if there was a constant instead of y like:
d/dx 4^3
it would have been Zero right?

yes I'm doing implicit differentiation and I don't know what it is though,

4. ## Re: what will this d/dx y^3 be?

and what would be
d/dx y
just y.

5. ## Re: what will this d/dx y^3 be?

Yes, if y is a constant, then it would be zero. However, in an implicit relation, it is implied that y depends on x. So, you would use the form in my first post above.

6. ## Re: what will this d/dx y^3 be?

so if they declare y as constant

this would become zero as well right? d/dx y^3

7. ## Re: what will this d/dx y^3 be?

Normally you would only treat y as a constant when doing partial differentiation. And you don't know what $\displaystyle \frac{dy}{dx}$ is, this is normally what you are trying to express as a function of x and y.

8. ## Re: what will this d/dx y^3 be?

It depends on whether you are trying to do a total derivative or a partial derivative. If it's a total derivative, use implicit differentiation. If it's a partial derivative, treat y as a constant.

9. ## Re: what will this d/dx y^3 be?

Normally, "y" is used as a variable or function of x. You have been told repeatedly that if y is independent of x, then so is f(y) for any f and so df(y)/dx= 0. If, however, y is itself some function of x, then df(y)/dx= (df/dy)(dy/dx), by the chain rule.

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# d/dx (y)

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