Question

71st derivative of the function 𝑓(𝑥) = sin^4 x − cos^4 x when x =(𝜋)/2, So, your challenge is to look for patterns to determine the 71st derivative of the above function evaluated at x =(𝜋)/2.

Answer 1

so, did you look for a pattern?
The first thing to note should be that
sin^4 x − cos^4 x = sin^2x - cos^2x = -1/2 cos2x
So now it becomes easy
f^⁽¹⁾ = -1/2 (-2 sin2x)
^⁽²⁾ = -1/2 (-2^2 cos2x)
f^⁽³⁾ = -1/2 (2^3 sin2x)
f^⁽⁴⁾ = -1/2 (2^4 cos2x)
now finish it off