Question

For the given functions, (a) express dw/dt as a function of t, both by using the chain rule and by expressing w in terms of t and differentiating directly with respect to t.

Answer 1

To express dw/dt, we can use the chain rule or express w in terms of t and differentiate directly.

Step-by-step explanation:

To express dw/dt, we will use both the chain rule and express w in terms of t and differentiate directly.

Using the chain rule, if w = f(g(t)), then dw/dt = f'(g(t)) * g'(t). Here, let's say w = f(t), so dw/dt = f'(t).

Alternatively, we can express w in terms of t and differentiate directly. For example, if w = t^2, then dw/dt = 2t.