Final answer:
To find dz/dt using the chain rule, substitute the given values for x and y into the expression for z, then differentiate the resulting expression with respect to t using the chain rule.
Step-by-step explanation:
To find dz/dt using the chain rule, we need to express z in terms of t. Given z = sin(x)cos(y), and x = t, y = 2t, we substitute these values into the expression for z to get z = sin(t)cos(2t). Now, we can differentiate z with respect to t using the chain rule. The derivative dz/dt is found by taking the derivative of sin(t)cos(2t) with respect to t, which results in dz/dt = cos(t)cos(2t) - sin(t)(-2sin(2t)). Simplifying further gives dz/dt = cos(t)cos(2t) + 2sin(t)sin(2t).