Differentiation

Alan could you take a look at this answer please?

y=5tan(x) (a) Find the differential (b) Evaluate dy and Δy when x=π/4 and dx=−0.2

\(y=5tan(x)\\ \frac{dy}{dx}=5sec^2(x)\\ dy=5sec^2(x)dx\\ when \;\;x=\pi/4\;\;and\;\;dx=-0.2\;\;then\\ dy=5sec^2{(\pi/4})\times -0.2\\ dy=5*2\times -0.2\\ dy=-2\\ ~\\ \text{mmm... don't know about }\triangle y ...\)

I assume delta y = tan(pi/4 - 0.2) - tan(pi/4) ≈ -1.685

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I don't understand Alan :(

Thanks for answering though - maybe it will make more sense to me in the morning  ://