Question

Differentiate the function y = tan2(x)
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Answer 1

To differentiate the function y = tan2(x), we can apply the chain rule. The derivative of y with respect to x is 2tan(x)sec^2(x).

Step-by-step explanation:

The function y = tan2(x) is the square of the tangent function. To differentiate it, we can use the chain rule. Let u = tan(x), then y = u^2. Now, we can differentiate y with respect to u and u with respect to x:

1. dy/du = 2u
2. du/dx = sec^2(x)

Then, we can apply the chain rule:

dy/dx = (dy/du)(du/dx) = 2u(sec^2(x)) = 2tan(x)sec^2(x).