Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1), and c = (1,2, 2). r'(t) = ( 16+16t %3D %3D 11+14t -15-18t

Q: 2 Suppose that A = 3xyz²7 + 2xy³j - x²yzk and p = 3x² - yz. Find, at the point (1,-1, 1), 2.1 Vo,…

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Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

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Q: y - 2)2 + (x-2)2 . Find the direction of heat flow in the plate at the point (2, 1). Heat flows in…

A: Introduction: The gradient of the temperature function at the point is the direction of the greatest…

Q: Q and Z are vector valued functions Q(-1) = , Q'(-1) = , Q''(-1) = Z(-1) = , Z'(-1) = , Z''(-1) =…

A: Given Q and Z are vector valued functions such that:Q-1=0,0,-2Q'-1=1,-1,-1Q''-1=3,2,-2 and…

Q: Find the derivative of the vector function r' (t) = (1/-2t r(t) = n(17t²)i + √13+tj + let k 4e^4

A: Find the derivative of the vector functionr(t)=ln17-t2i+13+tj+1e4tkr'(t)=ddtln17-t2i+13+tj+1e4tk

Q: 1 g(u) = V5и + 8 then g' (u) =

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: Find f '(2), where f(t) = u(t) v(t), ū(2) = (1, 2, -1), u' (2) = (3,0, 4), and v(t) = (t, t², t³).

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Q: value of the dir function

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Q: 2) r(1) = ti –t j-tk, t20 Draw the graph of the vector-valued function, explaining it in detail.

A: The general form of the parametric equation of the curve in three dimensional space is given by ,…