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.

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.

oobleck · Accepted Answer

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