Question

Lety = tan(2x + 4) Find the differential dy when x = 4 and dx = 0.1

Answer 1

Given:

`y=tan\left(2x+4\right)`

To find:

The differential when x = 4 and dx = 0.1.

Step-by-step explanation:

Differentiating with respect to x we get,

`\begin{gathered} (dy)/(dx)=sec^2\left(2x+4\right)\cdot(2) \\ (dy)/(dx)=2sec^2\left(2x+4\right) \\ dy=2sec^2\left(2x+4\right)dx.............(1) \end{gathered}`

Substituting x = 4 and dx = 0.1 in equation (1), we get

`\begin{gathered} dy=2sec^2(2(4)+4)\cdot(0.1) \\ dy=0.2sec^2(12) \end{gathered}`

Therefore, the differential is,

`dy=0.2sec^(2)(12)`

Final answer:

The differential is,

`dy=0.2sec^(2)(12)`