d/dx(tanx)=1/cos^2(x) Re-write the algorithm as if the parallel algorithm is true.

Question

Re-write the algorithm as if the parallel algorithm is true.

Answer 1

Can be written 

(d/dx)(tan(x))=sec²(x)

Not sure what you’re asking for but tan(x)=sin(x)/cos(x).

If u=sin(x) and v=cos(x), tan(x)=u/v.

du/dx=cos(x), dv/dx=-sin(x),

(d/dx)(u/v)=[v(du/dx)-u(dv/dx)]/v²,

(d/dx)(tan(x))=[cos²(x)-(-sin²(x))]/cos²(x)=

[cos²(x)+sin²(x)]/cos²(x)=1/cos²(x).