Question

How do you differentiate `y = sin^2 4x + 1/2 cos 8x`?

Answer 1

`dy/dx=0`.

Explanation:

`y=sin^2(4x)+1/2cos(8x)`
multiplying both sides by `2` we get `2y=2sin^2(4x)+cos(8x)`
we know the rule of trigonometric multiple angles:`2sin^2x=1-cos(2x)`
so`2sin^2(4x)=1-cos(8x)`
so the equation reduces to `2y=1-cos(8x)+cos(8x)`=`1`
differentiating both sides w.r.t `x` we get `dy/dx=0`.