If f(x,y) = sin (x,y), x = 3t and y = t^2. Consider z(t) = f(x(t),y(t)), for all t belongs to R.

(a) Calculate z'(t) directly.

(b) Calculate z'(t) using the chain rule.

Question

If f(x,y) = sin (x,y), x = 3t and y = t^2. Consider z(t) = f(x(t),y(t)), for all t belongs to R.

(a) Calculate z'(t) directly.

(b) Calculate z'(t) using the chain rule.

zepdrix · Answer

|dw:1349997938372:dw|
I think the chain rule should look something like this.
It's a little messy cause of the intermediate functions.
Lemme know if it's confusing.

I'm not sure what they're asking for in part a. Directly...?