Question

Evaluate the derivative of the function: y=sec^-1(7ln6x)

Answer 1

To evaluate the derivative of y=sec^-1(7ln6x), apply the chain rule. The derivative is given by dy/dx = 7/(x|x(7ln6)^2-1|√(x^2(7ln6)^2-x^2)).

Step-by-step explanation:

To evaluate the derivative of the function y=sec^-1(7ln6x), we can start by applying the chain rule. Let's break it down step by step.

1. First, apply the chain rule to the inverse secant function: d/dx(sec^-1 u) = 1/(|u|√(u^2-1)) * du/dx
2. Next, find the derivative of the expression inside the inverse secant function, which is 7ln6x: du/dx = d/dx(7ln6x) = 7 * d/dx(ln6x) = 7 * (1/x) = 7/x
3. Substitute the values back into the chain rule formula: dy/dx = 1/(|7ln6x|√((7ln6x)^2-1)) * (7/x)

Thus, the derivative of the function y=sec^-1(7ln6x) is given by dy/dx = 7/(x|x(7ln6)^2-1|√(x^2(7ln6)^2-x^2)).