Question

Suppose that x and y are differentiable functions of t and that z^{2}=x^{2}+y^{2} then {d z}{d t}= __

Answer 1

To find d z/d t when z^2=x^2+y^2, we can differentiate both sides of the equation with respect to t using the chain rule.

Step-by-step explanation:

To find d z/d t when z2 = x2 + y2, we can differentiate both sides of the equation with respect to t using the chain rule. Applying the chain rule, we have:

2z(d z/d t) = 2x(d x/d t) + 2y(d y/d t)

Dividing both sides by 2z gives us: (d z)/(d t) = x(d x/d t) + y(d y/d t).