Ufyukyu

3 1 $begingroup$ If the gradient only results in a vector telling you the steepest direction to travel, how can the "slope" in any direction be calculated? If the gradient is: $nabla f(x,y,z) = left[begin{array}{c}frac{partial f}{partial x}\frac{partial f}{partial y}\frac{partial f}{partial z} end{array}right]$ How can the directional derivative simply be a dot product between the gradient and the vector? $nabla_{vec{v}},f(x,y,z) = nabla f(x,y,z) cdot vec{v} = vec{v}_xfrac{partial f}{partial x}+vec{v}_yfrac{partial f}{partial y}+vec{v}_zfrac{partial f}{partial z}$ multivariable-calculus vectors partial-derivative vector-analysis share | cite | improve this question