Determine the instantaneous rate of change of y=tanx at x=1 to 3 decimal places
To determine the instantaneous rate of change of a function, we need to find its derivative. In this case, we want to find the derivative of y = tan(x).
The derivative of y = tan(x) can be found using the chain rule, which states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).
The derivative of tan(x) is sec^2(x). Therefore, dy/dx = sec^2(x).
Now, we can evaluate the instantaneous rate of change at x = 1. To do this, we substitute x = 1 into dy/dx = sec^2(x) to get the value of the derivative at that point.
dy/dx = sec^2(1)
To find the value of sec(1), we can use a calculator or a mathematical software. Evaluating sec(1) to several decimal places, we get sec(1) ≈ 1.850815717.
Therefore, the instantaneous rate of change of y = tan(x) at x = 1 is approximately 1.850 to 3 decimal places.