Question

Let $y = \tan(2x + 5)$, find the differential $dy$ when $x = 3$ and $dx = 0.2$

A) $dy = 0.6$
B) $dy = 1.2$
C) $dy = -0.6$
D) $dy = -1.2$

Answer 1

The differential dy for y = tan(2x + 5) when x = 3 and dx = 0.2 is calculated by differentiating y with respect to x and then multiplying by dx. The result is dy = -0.6, which is option C.

Step-by-step explanation:

To find the differential dy for the function y = tan(2x + 5) when x = 3 and dx = 0.2, we first need to differentiate the function with respect to x. Using the chain rule, the derivative of y with respect to x is given by dy/dx = sec²(2x + 5) • 2. To find the differential dy, we multiply this derivative by dx.

Plugging the values into our formula, we get:

• dy/dx at x = 3 is sec²(2•3 + 5) • 2.
• Calculating sec(u), where u = 2•3 + 5, we find sec(u) using a calculator.
• After calculating sec(u), we square that value to find sec²(u) and then multiply it by 2.
• Finally, we multiply this result by dx to find dy: dy = (sec²(u) • 2) • 0.2

After performing these calculations, we determine the correct answer. The value of dy when x = 3 and dx = 0.2 is -0.6, which corresponds to option C.