What is the derivative of y + x + y² = x ? O y : 1- 3z2 3y2 + 2y 1+ 3x? 3y? + 2y O y = 1- 3x2 3y? +y 1- 322 y? + 2y

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

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Q: What is the derivative of y = x cos"'(x²)? dy (VI-2²' ) cos' z²+21² dz (VI-zª ) cos' z² –2=² (VI-z4…

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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: Find the simplified form of the derivative of y = 1+csc 3x %3D cot 3x O y = 3 csc 3x csc(3r)-1 O (E)…

A: We have to find the simplified form of the derivative of  y = 1+csc 3xcot 3x.

Q: This is the complete problem. Calculate the derivative in respect to y of xy+2x^2 y−6y^3 x+y when…

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Q: Find the derivative of the function. A y = 7tan-(x - V1 + x²) %3D (2* * I^ -

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Q: Find the derivative of the function. 10) y = (x + 1)2(x2 + 1)-3 2(x + 1)(2x2 + 3x - 1) (x2 + 1)4…

A: Given:        y= x+12x2+1-3

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: 2. Calculate the derivative of the following. y = (x*- 3x2+5x) 3 y = tan (x2 + 5x - 2) А. B. (4x +…

A: Given  A. y=(x4-3x2+5x)3 B. y=tan2(x2+5x-2)C. y=(4x+3)3(x-2)2D. y=x2ex2-1

Q: what is the derivative of y=e^-1/2x(C1cos3x+C2sin3x) and evaluate if x=0, y'=8

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Q: Find the derivative of y = 3x ln (x)? A. Y = 3(1+ ln (x)) B. Y = 3 + In (x) C. y = 1+3 ln (x) D. Y =…

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Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

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Q: Find the derivative of y with respect to x if y = (13x - 26x+26) e -8x y =D %3D

A: Explanation of the answer is as follows

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

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Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: use product rule, find derivative of x.y3 O 1.y3 + x. 3y2y' O 1.y° + x. 3y? O x. 3y2y' noe of the…

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Q: compute the derivative indicated. g(x, y, z) =x2 + y2 + z2, gxyz

A: Given function g(x, y, z) = x2 + y2 + z2

Q: 20. Find the derivative of the function. y = 9cos(2x) a. y'=-18sin(2x) b. y' =18sin(2x) c.…

A: Option (a) is the correct option. Differentiate y using the chain rule.…

Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

Q: Find the derivative of y with respect to x. 6х + 11 y = - csc 7 O A. 42 |6x + 11|V(6x + 11)2 – 49 O…

A: ddx(cosec-1x)=-1xx2-1

Q: What is the derivatives of f(x)=(x^3)/(9-X^2) and its x and y intersect?

A: a) From the given problem: fx=x39-x2Ory=x39-x2   So,   dydx=ddxx39-x2=ddxx39-x2-ddx9-x2x39-x22…

Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z - 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: Find the derivative of y with respect to x if y = (12x - 24x + 24) e - 3x. y' =D %3D

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Which among the choices has the first derivative that is equivalent to (2x + 1)(x + 2) ? Of (2)…

A: Solution:-  Step:1    Given:  f'x=2x+1 x+2

Q: Which of the following values is the directional derivative of f (x, y) = 3x² + xy – 2y² – yz + z?…

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Q: Calculate the second derivative of the function y = f (x) defined by the equation x³ + y +3xy + 3y²…

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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: Find the derivative of y with respect to the independent variable. y = 2ln 2t 2 In 2 t OB. 2In 2t In…

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Q: 4. y2 +2xy 4, find y" Ans. y" = (x+y)

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Q: y^2 = x^2 +xy

A: Differentiating both sides of the equation.

Q: Find the second derivative (y”) of 4x2 + 9y2 = 36 by implicit differentiation. a. -16y3/9      b.…

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Q: Suppose x and y are variables (y is a function of x) that satisfy the equation x2-y= 12, What is…

A: Given that: x2-y3=12

Q: Use Quotient Rule to find the derivative. x² + x - 2 3x +1: dy 2x+1 A. dx 3x + 1 dy B.…

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Q: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Find the second derivative of vx - Jy= 4 when x = 1. 2 1 -1 -2

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Q: y" – 4y' +4y = 0; y(0) =-1, y'(0) = 0

A: We have to solve the differential equation…

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x? – 1)³(x² + 3)? x3+4x…

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Q: Find the derivative of ƒ(z)= 5z10 – 23 +2 f' (z) = %3D

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Q: 3r %3D 5r + 2 – 1 (d) f(x) =

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Q: What is the derivative of y (2æ)* O (2x)^(x) (1-2 In2x) O (2x)^(x) (1-In2x) O (2x)^(x) (1+2 In2x) O…

A: Given; y=(2x)x.

Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

Q: I. Find the derivative of y with respect to x. using inrement method x +7 1. у%3х? -3х -5 2. y = Зх…

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Q: What is the derivative of y = (sin (3x?)2? dy dr 12z sin' (3교2) VI-974 dy dr 12z sin (3z²) VI-9z4 dy…

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Q: What is the derivative of y = (2x)" O (2x)^(x) (1-In2x) (2x)^(x) (1+2 In2x) (2x)^(x) (1+In2x) O…

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Q: 2-х Find the derivative of y = Зx+1 -7 бх-5 6- А. (3х+1)2 В. (3x+1)2 7-6х С. (3x+1)2 D. (3x+1)2 Е.…

A: Proceed as shown below

Q: Find the derivative of f(z)=((11z+4)1/2)(e3z).

A: Given function f(z)=11z+412e3z