Find D_u f at P. f (x, y) = (1 + x y)^{3 / 2}, P (1, 3) ; u = 1 / {square root 3} i + 1 / {square...
Question:
Find {eq}D_u f {/eq} at {eq}P {/eq}.
{eq}\displaystyle f (x,\ y) = (1 + x y)^{\frac 3 2},\ P (1,\ 3)\ ;\ u = \dfrac 1 {\sqrt 3}\ \mathbf i + \dfrac 1 {\sqrt 3}\ \mathbf j {/eq}.
Directional Derivative:
The rate from which the function alters along the direction is known as the directional derivative. The directional derivative of a function shows the rate of change in any given direction. By having directional derivatives in each direction, calculus does not automatically imply differentiability.
Answer and Explanation: 1
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View this answerHere, {eq}\displaystyle f (x,\ y) = (1 + x y)^{\frac 3 2},\ P (1,\ 3)\ ;\ v = \dfrac 1 {\sqrt 3}\ \mathbf i + \dfrac 1 {\sqrt 3}\ \mathbf j {/eq}
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Chapter 14 / Lesson 6In this lesson, learn about directional derivatives, gradients, and maximum and minimum critical points. Moreover, learn to use the directional derivative formula to calculate slopes at given points.