Find the directional derivative of f(x,y,z)=xy+z^2 at the point (1,2,3) in the direction of a vector making an angel of pi/4 with gradf(1,2,3).
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Originally Posted by mgwalker Find the directional derivative of f(x,y,z)=xy+z^2 at the point (1,2,3) in the direction of a vector making an angel of pi/4 with gradf(1,2,3). As $\displaystyle f$ is differentiable at $\displaystyle (1,2,3)$ the directional derivative in the direction of $\displaystyle u\;(||u||=1)$ is $\displaystyle (\nabla f)(1,2,3)\cdot u=|| (\nabla f)(1,2,3) ||\;||u||\cos (\pi/4)=\ldots$
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