Question

What is the derivative of the function y = sec() ( − tan())?

(a) sec()² ( − tan()) – sec() ( − tan())²
(b) sec() tan() + sec()² ( − tan())
(c) sec() tan() – sec()² ( − tan())
(d) sec() ( − tan()) + sec()² ( − tan())

Answer 1

The derivative of the function y = sec() ( - tan()) is sec() tan() - sec()^2( - tan()). This is found by applying the product rule to differentiate each function separately and combining the results.

Step-by-step explanation:

The question asks for the derivative of the function y = sec() ( - tan()). To find the derivative, we will apply the product rule, which states that for two functions u(x) and v(x), the derivative d(uv)/dx is u'(x)v(x) + u(x)v'(x). In our case, u(x) = sec() and v(x) = -tan(). The derivative of sec() is sec() tan(), and the derivative of -tan() is -sec()^2(). Applying the product rule, we get sec()(-sec()^2()) + sec() tan()*(-tan()), which simplifies to sec() tan() - sec()^2( - tan()).