If f(x)= cos x , find f^(25) x

Answer 1

f(x) = cosx

f'(x) = -sinx

f"(x) = -cosx

f'''(x) = sinx

f⁽⁴⁾(x) = cosx

f⁽⁴⁾(x) = f⁽⁸⁾(x) = f⁽¹²⁾(x) = .... f⁽²⁴⁾(x) = ...

So, f⁽²⁵⁾(x) = [f⁽²⁴⁾(x)]' = (cosx)' = -sinx