Higher Order Derivative

Question

Find the given higher-order derivative.

f ″(x) = −cos(x),   f ⁽⁸⁾(x)

Answer 1

f^"(x) =-cosx

ever 4 derivative it's the same

f^{vi(x) also =- cosx}

7the derivative = sinx

8th = cosx

f⁽⁸⁾= cos(x)

or you could have worked backwards, integrate twice, f(x) = cosx (ignore the unknown constants)

then

8 derivatives of f(x) = cos(x)