10. Find the derivative of y = V3x + 2. c) d) 3x a) 2V3x+2

Q: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

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Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

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Q: Find the equation of the tangent line to f(x) = 2x* – 5xat x = 1. - Oy=3x+10 Oy=6x+19 Oy=6x-9 O…

A: Given equation: f(x)= 2x4- 5x f(1)= 2(1)4- 5(1)= -3

Q: 4. [ ]Find the derivative of y with respect to the given independent variable: Ins 7x (a) ex³y = 2x…

A: Given equation ex2y=2x+2y   As per our guideline, we  supposed to answer only the first three…

Q: usk 2: Find the derivative of 4x2 + 6y3 = 50 by filling the blanks. %3D (2 xD(x-)+x 6)(y³4)_=__ dy >…

A: We have, 4x2+6y3=50            ⋯⋯1 We know that, from basic derivative formula ddxkxn=n·kxn-1ddxk=0…

Q: In what directions is the derivative of ƒ(x, y) = (x2 - y2 )/ (x2 + y2 ) at P(1, 1) equal to zero?

A: Given, , the unit vector is , here directional derivative is given as,

Q: In the integration What is the implicit derivative of u? V9-4x² a. du = 2dx %3D b. du = * c. du =-…

A: dx9-4x2=dx32-2x2 Put, u=2x⇒dudx=21⇒du=2 dx

Q: z = Vx4 + yf, fz (1, 2)

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Q: (c) Compute the derivative of u = Vt² +2vt³.

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Q: Find the derivative of y = = Ve-5t +1 dy dt ||

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Q: 2. Calculate the derivative of the following. А. y = (x* – 3x² + 5x) ³ DUKAS B. y = tan²(x² + 5x –…

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Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

A: We will find the derivative of right side. By showing this derivative equal to integrand the…

Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

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Q: Let f(x, y) = V xy. Find the derivative of f. af 1 ду 2

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Find the derivative of the function y = In(3t + 4). %3D dy dt

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Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: y" +6y' +10y=0; y(0) = 2, y'(0) =

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Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: _6. What is the derivative of f(x) = (5 – x²)²? а. 2(5- х2) b. 10 – 2x2 C. 4x3 – 20x d.(5 - x?)(5 -…

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Q: What is the derivative of y = sin1 (x² + 2)? dy dr /1-(z²+2)² dy O dr 2x V1-(2²+2)² O dz V1+(x²+2)²…

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Q: 2. What is the equation of the tangent line to the curve y = x? - 2x +1 at point (3,4)? а. у3 2x — 2…

A: The equation of line is y-y1=mx-x1, where m is the slope of the curve.

Q: 6. Compute and write the slope of the tangent lines to dx y - xy +6 = 0 at the point (5,2). a. b. 2y…

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Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Compute each derivative. 4.3 1. dy (3r°y7-32r y3 + 5xy) 3x abc 2. Zz if z = 2x2ay

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Q: What is the derivative of y e3a + 1 3e3 %3D (e + 1) 3e3z (e + 1) O y = 12e6 +3e3 %3D (ed + 1) O y =…

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Q: With respect to u, what is the derivative of: * 12 בV 2 2 dx Option1 Option3 -'/2 -15

A: Answer is mentioned below -

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

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Q: In the integration What is the implicit derivative of u? V9-4x* a. du = 2dx b. du = * c. du =– 2dx…

A: Implicit differentiation of integral

Q: Compute the derivative of g(æ) = e dt. 22 -2xe -2xe O -2re

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Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Find Zxx=Zyy=Zxy=

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Q: Use the definition of the derivative to compute dy/dx. y=2x^2-3x+1

A: Use the definition of the derivative to compute dy/dx. y=2x^2-3x+1

Q: Find the derivative of y with respect to x. 6 y = (x³ In x) %3D dy dx II

A: Please see the below picture for detailed solution.

Q: Find the derivative ofy. with respect to x if y=(Ix +5) (9x² +2x) %3D

A: Given that: y=(x+5)(9x2+2x)

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: Find all (x,y) points where x² +4y² +4x- 8y+4 = 0 has horizontal or vertical tangent lines.

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Q: 3. Find the total derivative of V with respect to X. V=3X³ +5Y²+6Z Z=4+5X Y=3X+6Z+5XZ

A: Given, V=3X3+5Y2+6ZZ=4+5XY=3X+6Z+5XZ

Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: Find the derivative, or y', of ³ – Vy = ¿y² + 6 at (2,1).

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Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

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