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

Lety = tan(2x + 4) Find the differential dy when x = 4 and dx = 0.1-example-1
User Mushrankhan
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1 Answer

25 votes
25 votes

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)
User Daniel Marcus
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