Does the Chain Rule Apply to This Derivative?

[asi123]

Homework Statement

Guys, is this right?
And if it is, from the the y' got in there?

Homework Equations

The Attempt at a Solution

 

[rootX]

Homework Statement

Guys, is this right?
And if it is, from the the y' got in there?

Homework Equations

The Attempt at a Solution

You should use imageshack/other for images

 

[statdad]

The answer looks reasonable - perhaps multiply the two negatives.
I'm not sure what you mean by "And if it is, from the the y' got in there?"

 

[HallsofIvy]

Here, z and y are both functions of some other variable, perhaps x or t. If z= f(y) and y is itself a function of x, then, by the chain rule
$$\frac{dz}{dx}= \frac{dz}{dy}\frac{dy}{dx}$$

If, in particular, z= sin(1/y)= sin(y^-1), and y is a function of x, then
$$\frac{dz}{dx}= cos(1/y)(-1/y^2)\frac{dy}{dz}$$
or, the ' notation,
z'= cos(1/y)(-1/y²)y'= (-cos(1/y)/y²)y'