Directional Derivative question?
The derivative of f(x,y) at P(1,2) in the direction of i + j is 2√2 and in the direction of -2j is -3. What is the derivative of f in the direction of –i – 2j ? Give reasons for your answer.
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Since we're at a fixed point, just use linearity.
In other words, as -i - 2j = -(i + j) + (-1/2) (2j),
the derivative in the direction of -i - 2j = - (2√2) + (-1/2) (-3) = 3/2 - 2√2.
I hope that helps!