Chain rule?

**No Logic Sense** · February 23rd 2009, 04:59 AM

Ok, so in an equation I have the following:
$y^2$

If I want to find the derivative of this, I figured I should use the chain rule on this one:
$\frac{dy}{dy} \cdot \frac{dy}{dx}=1 \frac{dy}{dx}$

But is that correct? I don't get it if it's wrong. :/

**Amanda H** · February 23rd 2009, 05:57 AM

The answer you got is almost right. It should be:
$2y\frac{dy}{dx}$
I'm going to name this equation as follows
$f = y^2$
I'm using f instead of the traditional y so the equation makes sense

The chain rule states $\frac{dy}{dx} = \frac{dy}{du} * \frac{du}{dx}$

In your case where $u = y$
$f = u^2$
$\frac{df}{du} = 2u$

Then when:
$u = y$
$\frac{du}{dx} = \frac{dy}{dx}$

So using the chain rule in this case you get:
$\frac{df}{dx} = \frac{df}{du} * \frac {du}{dx}$
$\frac{df}{dx} = 2u * \frac{dy}{dx}$
Substituting y back in it becomes:
$2y\frac{dy}{dx}$

You had the right idea and almost got it correct. The chain rule can be easy to mess up especially when y is involved.

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