Question

Find the differential of the function y = tan(7t).

Answer 1

The differential of the function
`y = tan(7t)` is found by differentiating it with respect to t, resulting in
`dy = 7 * sec^2(7t) dt`, using the chain rule.

Step-by-step explanation:

To find the differential of the function
`y = tan(7t)`, we will differentiate the function with respect to t.

We recall that the derivative of tan(x) is
`sec^2(x)`, and by using the chain rule, we differentiate the inside function, which is 7t.

Thus, the derivative of y with respect to t is
`dy/dt = 7 * sec^2(7t)`.

Therefore, the differential, often denoted as dy, is
`dy = 7 * sec^2(7t) dt`, which expresses how the function y changes in response to a small change in t.