![y=sinx,求n阶导数](/zb_users/upload/2023/10/f0e2225c731311eea9c65254000ebf90.jpeg)
y=sinx的n阶导数为y⁽ⁿ⁾=sin(x+nπ/2);
解析:因为y'=cosx=sin(x+π/2);
y''=-sinx=sin(x+2*π/2);
y'''=-cosx=sin(x+3*π/2);
所以可得:y⁽ⁿ⁾=sin(x+nπ/2);
y=sinx的n阶导数为y⁽ⁿ⁾=sin(x+nπ/2);
解析:因为y'=cosx=sin(x+π/2);
y''=-sinx=sin(x+2*π/2);
y'''=-cosx=sin(x+3*π/2);
所以可得:y⁽ⁿ⁾=sin(x+nπ/2);