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