Let y=tan(5x+8).Find the differential dy when x=4 and dx=0.1 Find the differential dy when x=4 and dx=0.2

Question

Let y=tan(5x+8).Find the differential dy when x=4 and dx=0.1   Find the differential dy when x=4 and dx=0.2

Answer 1

Here y = tan (5x + 8) or

sin (5x + 8)

cos (5x + 8)

Take dy/dx as {cos (5x + 8) d[sin (5x + 8)]/dx − sin (5x + 8)d[cos (5x + 8)]/dx} ÷ cos²(5x + 8)

which goes to 5 cos²(5x + 8) + 5 sin²(5x + 8) ÷ cos²(5x + 8) or 5/cos²(5x + 8).

Then write dy = 5dx/cos²(5x + 8).

For (x, dx) = (4, 0.1), obtain dy = 5(0.1)/cos²(28). For 28 in Radian Measure,

dy calculates to 0.5396013112.

For (x, dx) = (4, 0.2), obtain dy = 5(0.2)/cos²(28). For 28 in Radian Measure,

dy calculates to 1.079202622.