27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0

Q: Find the partial derivative fx and fy of the given function 3x f(x, y) = -y2 :/ cos(r? – - t + 1)dt.

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Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: Find the point D'4, symmetric of D4 with respect to the line F4B1. F4: (-2,1,3) D4: (1,2,3) B1:…

A: Here we will find poinr D'4 symmetric of D4

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: with y(0) -1

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Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

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Q: Find dy/dx given xy2 + x²y5 – x³ = 3 %3D -

A: Given that : xy2 + x2 y5 - x3  = 3. Find dy/dx . We know that d(xn)/dx = nxn-1.   Here i attached…

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: 13. Find ƒ. (1)ƒ'(x)=x² + 3√x (2) f(t)=2cost+sec²t,-/2 <t</2,ƒ(π/3)=4; (3)ƒ*(x) = 6x+sinx.

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Q: 4) Let f(x) = - ax"+1 and a x) = 4X-3 5:) f(x) = Fxan? find the 3 first f,g and h. uch that (fo gohl…

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Q: Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the…

A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: Find the value of fææ + fyy at (1, –1) when 3 + x² + 2y?. xy f(x, y) 1. (frr + fyy)- -7 |(1,–1) 2.…

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Q: The function z(x, y) obeys, = -2e Which of the follow represents a valid first step for finding u(x,…

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Q: 1) fix) = (x-2).x+1 find the maximum,minimum and inflection paints of the finction. %3D

A: An inflection point is a point at which the second derivative is equal to zero or is undefined and…

Q: By using chain rule Find dy/dx iff- u=-1, x=-1

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Q: よ2 et + 1 lim xー0 |x2 dt = ? 1+ v2 + et 1.

A: We will use DL hospital rule and leibniz rule to solve this question.

Q: A dilation T sends A = (2,3) to A’ = (5,4), and it sends B = (3,−1) to B’ = (7,−4). Where does it…

A: We have, A dilation T sends A = (2,3) to A’ = (5,4) and it sends B = (3,−1) to B’ = (7,−4) Where…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = e-xyz

A: Given fx,y,z=e-xyz Partial derivative means differentiating with respect to one variable keeoing…

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: nd

A: Find dydx, for y=ln(tet), x=etan-1(2t)

Q: Find given that y=[atan-¹(bx)]². dy dx Assume a,b ER. 2[atan-¹(bx)] O 2[atan-¹(bx)]- O 2b[asec²(bx)]…

A: To find dydx given that y=a tan-1bx2.Assume a, b∈ℝ

Q: 6. dx = x + 4x + 5 (A) arctan(x + 2) + C (B) arcsin (x + 2) + C (C) In|r*+ + 4x + + C 1 (D) + C x° +…

A: Proceed as shown below...

Q: (b) 9-(t+1) (42t - sin t)dt

A: Given that the integral is .The objective is to evaluate the given integral.

Q: dz (е) dz

A:

Q: 6. The equation 16 - 2 = 0 defines z as a function of x and y. Find az/dx and az/dy at the point (9,…

A: Given: The equation 6x+16y+2z-2=0 defines z as a function of x and y. To Find: ∂z∂x and ∂z∂y at the…

Q: Find whether the function F= 5yz? i+(3x– 2)}+(x² – xyJk is solenoidal.

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Q: Calculate Vf when f 3x 2- y z' + 4x'y + 2x - 3y - 5 at the point (1, 1, 0).

A: