# Homework Help: Find f'(1), ∂g/∂s(1, 1), and ∂g/∂t(1,1).

1. Apr 16, 2012

### s3a

1. The problem statement, all variables and given/known data
The problem is attached.

f'(1) = -68
∂g/∂s(1, 1) = 14
∂g/∂t(1, 1) = -136

2. Relevant equations
Differentiation and partial differentiation.

3. 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!

#### Attached Files:

• ###### Problem.jpg
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2. Apr 16, 2012

### 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.

3. Apr 16, 2012

### tazzzdo

Wait I misread this. Something is off...

4. Apr 16, 2012

### s3a

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