{\displaystyle {\begin{aligned}{\boldsymbol {x}}^{(k+1)}&={\boldsymbol {x}}^{(k)}-\alpha \operatorname {grad} f({\boldsymbol {x}}^{(k)})\\&={\boldsymbol {x}}^{(k)}-\alpha {\begin{bmatrix}{\dfrac {\partial f({\boldsymbol {x}}^{(k)})}{\partial x_{1}^{(k)}}}\\{\dfrac {\partial f({\boldsymbol {x}}^{(k)})}{\partial x_{2}^{(k)}}}\\\vdots \\{\dfrac {\partial f({\boldsymbol {x}}^{(k)})}{\partial x_{n}^{(k)}}}\end{bmatrix}}\end{aligned}}}