Question

Use the chain rule to find ∂z/∂s and ∂z/∂t. Given z = tan(uv), where u and v are variables.

Answer 1

To find ∂z/∂s and ∂z/∂t, differentiate z with respect to u and v separately and apply the chain rule.

Step-by-step explanation:

To find ∅z/∅s and ∅z/∅t using the chain rule, we first need to differentiate z with respect to u and v separately. Recall that tan(uv) is equivalent to tanu * tanv. So, let's differentiate tanu and tanv:

1. Differentiate tanu: ∅(tanu) = sec²u * u'
2. Differentiate tanv: ∅(tanv) = sec²v * v'

Now, we can apply the chain rule. ∅z/∅s = ∅z/∅u * ∅u/∅s = sec²u * u' * v' and ∅z/∅t = ∅z/∅u * ∅u/∅t = sec²u * u' * v'.