Find f'(1), ∂g/∂s(1, 1), and ∂g/∂t(1,1).

[s3a]

Homework Statement

The problem is attached.

The correct answers are:
f'(1) = -68
∂g/∂s(1, 1) = 14
∂g/∂t(1, 1) = -136

Homework Equations

Differentiation and partial differentiation.

The Attempt at a Solution

I'm at the f'(1) part. I differentiated each component of F(2 – 3t + 2t^2, 19 – 27t + 9t^2, -4 + 3t + 2t^2) to get f'(t) = F(-3 + 4t, -27 + 18t, 3 + 4t) and then f'(1) = F(1, -9, 7). I'm not entirely certain if what I did is correct so far. If it is, what do I do next? If I omitted something important, tell me.

Any help in solving this problem would be greatly appreciated!
Thanks in advance!

 

[tazzzdo]

Looks fine to me.

Now differentiate the components of g(s,t) first with respect to s, then with respect to t, and plug in (1, 1) just like before.

 

[tazzzdo]

Wait I misread this. Something is off...

 

[s3a]

My answer differs from the correct answer quite a bit ;). Thanks anyways though.

If someone else knows, please help me.