Let y=tan(5x+2). Find the differential dy when x=2 and dx=0.4Find the differential dy when x=2 and dx=0.8

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You need to remember that the tangent function is rational, hence you should write the tangent function as `tan(5x+2) = sin(5x+2)/cos(5x+2)` .

You need to find dy, hence you need to differentiate with respect to x using quotient rule such that:

`dy = (sin(5x+2)/cos(5x+2))dx`

`dy = (5cos(5x+2)*cos(5x+2)+ 5 sin(x+2)*sin(x+2))/(cos^2(5x+2))dx`

You need to factor out 5 such that:

`dy = 5(cos^2(5x+2) + sin^2(x+2))/(cos^2(5x+2))dx`

You...

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