Answer
Using the definition of dot product we show that the directional derivative ${D_{\bf{u}}}f$ is equal to the component of $\nabla f$ along ${\bf{u}}$.
Work Step by Step
Let ${\bf{u}}$ be a unit vector. Then by Theorem 3, the directional derivative ${D_{\bf{u}}}f$ is given by
${D_{\bf{u}}}f = \nabla f\cdot{\bf{u}}$
By definition of dot product, ${D_{\bf{u}}}f$ is equal to the component of $\nabla f$ along ${\bf{u}}$.
