Find the directional derivative of f at the given point in the direction indicated by the angle θ. f(x, y) = 8x + 9y , (9, 1), θ = −π/6

The directional derivative of f is 4√3 - 9/2

Step-by-step explanation:

∵ Du f(x,y) = fx(x,y) · a + fy(x,y) · b

∵ The unit vector in the direction of Ф is <a , b>

∵ f(x , y) = 8x + 9y at the point (9 , 1) in the direction Ф = -π/6

∵ df/dx = 8 , df/dy = 9

∴ Du f(x,y) = 8 · a + 9 · b

∵ The unit vector U = <cos(-π/6) , sin(-π/6)> = <√3/2 , -1/2>

∴ Du f(9,1) = 8(√3/2) + 9(-1/2) = 4√3 - 9/2

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step-by-step explanation:

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step-by-step explanation: