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Lety = tan(3x + 3) . Find the differential dy when x = 5 and dx = 0.4

Lety = tan(3x + 3) . Find the differential dy when x = 5 and dx = 0.4-example-1
User Shihab Uddin
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1 Answer

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Applying the derivative of the trigonometric functions, the derivative of tan x is sec²x.

Hence, the derivative of tan (3x + 3 ) is sec² (3x + 3) times the derivative of 3x - 3 which is 3.


\begin{gathered} y=tan(3x+3) \\ dy=3sec^2(3x+3)dx \end{gathered}

To find the differential dy when x = 5 and dx = 0.4, simply replace the x and dx in the dy function with their given values.


dy=\lbrace3sec^2[(3(5)+3)]\rbrace(0.4)

Then, simplify.


dy=[3sec^2(18)](0.4)
dy=3.3167(0.4)
dy=1.32668\approx1.33

Hence, at x = 5 and dx = 0.4, the differential dy is approximately equal to 1.33.

For x = 5 and dx = 0.8, we do the same process above but this time, multiply the derivative by 0.8.


dy=[3sec^2(18)](0.8)
dy=3.3167(0.8)
dy=2.6534\approx2.65

Hence, at x = 5 and dx = 0.8, the differential dy is approximately equal to 2.65.

User Furkan Ayhan
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