Find the directional derivative of the function at the point Pin the direction of the unit vector u = cos ôi + sin 0j. Sketch each the graph of the function, the point P, and the unit vector u. 3. f(x,y) = 3x – 4xy + 9y, P(1, 2), v =i+j.

Q: determine directional derivative f(x, y) = x²y³ – 4y on point (-1,2) on vector direction v = (2, 1).…

A: The partial derivatives of f at (x,y)=(-1,2) are : ∂f∂x=2xy3   and   ∂f∂y=3y2x2-4. Therefore,…

Q: t3 Find the vector equation of the tangent line to 7(t) = 2 (e1-t) In t i+ tan-1 tj+ k at cos(t n)…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 8t – t³, In(t))

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Q: At the point P(1,2, 3), a function f(z, y, z) has directional derivative of-4 in the direction…

A: We have to find the value of fy(P).

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Find the derivative, r'(t), of the vector function. r(t) = t* i + cos(t³) j + sin?(t) k

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Q: Gradient. Directional Derivative Find the directional derivative of f(x, y, z) = 2x2 + 3y2 + z2 at…

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Q: erivative f 3i-4j i

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Q: ii) xy5/2+x³/2y 12. Point (4, 1). d²y Ex 3. Calculate the second derivative for the following: dx2…

A: The given equations are

Q: Ex 1. Calculate the derivative i) x² + y² = 1. dy 33 dx for the following: ii) xy= x²+y.

A: To calculate the derivative  of the following.

Q: Find the second derivative. y = 6x° - 5x² + 3 e * O A. 24x- 10 - 3 e* O B. 10x-24-3 ex O C. 36x - 10…

A: To find the second derivative: y=6x3-5x2+3ex Solution: y=6x3-5x2+3ex Differentiating both sides…

Q: Suppose that distances are measured in lightyears and that the temperature T of a gaseous nebula is…

A: Suppose that distances are measured in lightyears and the temperature T of a gaseous nebula is…

Q: Determine if the equation (x* +y°) dx + (5xy* +y°) dy = 0 is exact. Identify M = and N = ƏM ƏN The…

A: For differential equation ,M dx + N dy=0 is to be exact if∂M∂y=∂N∂xthen solution is∫ M dx + ∫ N…