Question

Let y = tan(2x + 6). Avoid rounding until the last step and round your answers to at least 3 decimal places. Find the differential dy when x = 5 and dx = 0.2.

Answer 1

The differential dy when x = 5 and dx = 0.2 is 0.448.

Step-by-step explanation:

Let y = tan(2x + 6). We need to find the differential dy when x = 5 and dx = 0.2. To find dy, we need to use the chain rule.

According to the chain rule, the differential dy is given by dy = (dy/dx)*dx. Here we have dy/dx = 2*sec^2(2x + 6). When x = 5, dy/dx = 2*sec^2(14). Now we can substitute this value of dy/dx and dx in the equation dy = (dy/dx)*dx to find the differential dy.

Thus, dy = (2*sec^2(14))*0.2. Solving this equation, we get dy = 0.448. Hence, the differential dy when x = 5 and dx = 0.2 is 0.448.