How do you find the derivative of y tan(2x)?

To find the derivative of the function y tan(2x), we need to apply the product rule of differentiation as well as the chain rule.

The product rule states that if you have a function that is the product of two functions, say u and v, then the derivative of their product is given by:

(uv)’ = u’v + uv’

In our case, let:

• u = y (where y is a function of x)
• v = tan(2x)

Now, we need to calculate the derivatives u’ and v’:

1. The derivative of y with respect to x is simply dy/dx (we’ll denote it as y’).

2. To differentiate tan(2x), we use the chain rule. The derivative of tan(u) is sec²(u) * du/dx. Here, u = 2x, so du/dx = 2. Thus,

v’ = sec²(2x) * 2 = 2 sec²(2x).

Now we can apply the product rule:

(y tan(2x))’ = y’ * tan(2x) + y * (2 sec²(2x))

So, the derivative of y tan(2x) is:

y’ tan(2x) + 2y sec²(2x).

This is how you find the derivative of the function y tan(2x).