Calc question?

Question

If anyone could explain how the following is done, it would be greatly appreciated!

Use the chain rule to find ∂w/∂s and ∂w/∂t.

w = pqsinr, p = 2s + t, q=s - t, r=st

Answer 1

You essentially have three functions multiplied together p,q,r.

To find a derivative take the power rule first: d(pqr) = dp qr + p dq r + pq dr with respect to your variable of choice (s or t)

Answer 2

∂w/∂s = 2qsinr + psinr +pq(cosr)(t)
∂w/∂t = qsinr + p(-1)sinr + pq(cosr)(s)
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Ideas: use chain rule ∂w/∂s = ∂w/∂p ∂p/∂s + ∂w/∂q ∂q/∂s + ∂w/∂r ∂r/∂s
The same approach can be applied to ∂w/∂t.