Question

Darivative of [{(sinx×sinx)+sinxcosx }/{(cosx×cosx)+sinxcosx}]=?

Answer 1

`d/dx (sinx sinx+sinx cosx )/(cosx cosx+sinx cosx) = sec^2x`

Explanation:

We seek the derivative of:

`y =(sinx sinx+sinx cosx )/(cosx cosx+sinx cosx)`

Which we can write as:

`y =(sinx (sinx+cosx) )/(cosx( cosx+sinx))`

`\ \ =sinx/cosx`

`\ \ =tanx`

Hence as this is a standard derivative, we have the trivial result:

`dy/dx = sec^2x`