d d Calculate r1(t) · r2(t)] and dt ri(t) × r2(t)] first by differentiating dt the product directly and then by applying the formulas dr2 = ri(t)- d dri ri(t) r2(t)] = r1 · r2(t) and dt dt dt d dr2 [r(t) x r2(t)] = ri(t) x dt dri x r2(t). dt dt ri(t) = cos(t)i + sin(t)j+5tk, r2(t) = 4i + tk d [r:(t) · r2(t)] = d Iri(t) x r2(t)] dt

Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function f(r) = VI+ tª dt.

A: We will use the first fundamental theorem of calculus to evaluate the derivative.   The detailed…

Q: Evaluate W(3,-1) for the function W(x,y) = 4x^2 + y^2

A: W(x,y) = 4x2 + y2Find W(3,-1)

Q: Calculate r' (t) and T(t), where r(t) = (2t - 7,2 – 5t, 3 + 5t). r' (t) = (2 T(t) = -5 5

A:

Q: find (f o g) (2): f(x) = x^2 + 1, g(x) =x -1

A: (f o g) (2) = f(g(2)) So we will find g(2) by plugging x=2 in g(x) g(x)=x-1 g(2)=2-1 g(2)=1

Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

A:

Q: (x+y)^2=x^2 + 2xy + y2, subsitute (-2) for x,and (-1) for y, and check if the left hand side is…

A:

Q: Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following: A. f(g(h(2))) B.…

A:

Q: D) Factor f (x) = x³ + 2x2 + 4x +8 into complex linear factors. %3D

A:

Q: r(4) (arcsin(t), arcos(1),0

A: Given: rt=arcsint, arccost, 0   As we know that; ddxarcsinx=11-x2ddxarccosx=-11-x2

Q: Let f(x, y) /150- 4а2 — 2у? 4x? – 2y? Evaluate f(1, 3)

A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

A:

Q: How can you apply the chain rule in calculus 3 with multivariable calculus

A:

Q: Use synthetic division to find 1"(-1) and f"(-1) where f(x)= 3x'-8x + 5x-2x' + 5x +13

A: To find the f'''-1 and f4-1 Given that the  fx=3x7-8x6+5x4-2x3+5x+13 f'x=21x6-48x5+20x3-6x2+5…

Q: Find the general solution u(x,y) of: uxy : 2y. =

A:

Q: Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following: A. f(g(-3)) B. f(h(7))…

A: I have given the answer in the next step. Hope you understand that

Q: h = (-6x³ + 9xª + 5x7) (7 + 5x – 4x?). Then h= fgwhere %3D f = and g = Using the product rule h'(x)…

A: differentiate this with product rule.

Q: Calculate fx(l, 3) and /y(l, 3) for f (x, y) =

A: Given: fx,y=7x+y2

Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

A:

Q: For which real number a, the solution of the Initial Value Problem is such that x(2) = e. O 1/4 02 O…

A:

Q: Determine whether the function f(z)=z^2+(bar z) is analytical at z=1+i, where (bar z) denotes the…

A: Analytical functions, also known as holomorphic functions, are complex functions that are…

Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: Simplify the expression xyz + x’y + x’y’

A: We have to simplify the expression xyz+x'y+x'y'.

Q: What kinds of changes occur in the Coefficients of a Nonbasic Variable when the original model is…

A: Answer is explained below

Q: Let y = xbex (where b is a real number). Determine y'.   Let y = (3x + 6)/(6x + 12). Determine y'.

A: given y=xbex to find the derivative y' use the product rule uv'=uv'+vu' therefore,…

Q: Let f(x, y) = √175 – 3x² – 4y² Evaluate f(5,3)

A:

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: Differentiate. 1) f(x) = 4x2 - 5x+4 A) f'(x) = 4x-5 2) y = (2x² + 3x)² A) B) f'(x) = 4x²-5 = 8x3 +…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find p′(t), p′′(t), and p′′′(t) for the function p(t) = t^(100)+ 4e^(t)+ 16. (You can use rules or…

A: The function is p(t)=t100+4et+16

Q: Find r'(t), r"(t), r'(t) ・r"(t), and r'(t) × r"(t). r(t) = 클레 - 3tj + (a) r'(t) (b) r"(t) (c)…

A: We need to find derivative and dot and cross products.

Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx