2. (a) This is correct. (b) This is correct. (c) This is incorrect. Because the differentiation is with respect to the variable x, the Chain Rule is needed to obtain d sin(y²) = 2y cos(y²)“Y dx dx

Q: 2. Find dy/dx (a) x = 5 sin 16t + 126 and y = 5 cos 16t + 13 (use parametric differentiation) (b)…

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Q: d 5x+3 4. dx 7x+2

A: As we know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 And c·f'=c·f' ; where…

Q: 9. The anti-derivative of the function f(x) = e² + cost is (a) e²+ sinx+c (b) e² - tanz+c 10. 0.5(x…

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Q: 12. cos cos (xy) = 1+ sin y

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Q: Can you help me with this problem step by step?

A: Given:

Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: Let y=(x2+3) to the 2nd power. Find the differential dy when x=4 and dx=0.2 ?????????? Find the…

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Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: Q: If In/x² + y2 =sec(), use implicit differential to proof the following dy _ -x(x²+y²). sec. tan?…

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Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: Find the differential equaiton corresponding th y= a cos(log x) +b sin(log x) where a and b are…

A: Differential equation formation

Q: 1. Find the y" of y = (4x - 3x + 1) (5x + 7) 2. Find y" given y = cosx + sin 3x 3. Find all the…

A:

Q: 5. As a particle moves through the first quadrant, its a and y coordinates are functions of time t,…

A: Given tan(theta)=y/x

Q: dw of w -+ dt X y H.W: Use the chain rule to find the derivative dw with x= cos 1, y = sin? t, z =-…

A: We differentiate the function with respect to t.

Q: 4 sin (2x) dx cos (2x)t4

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Q: Let z=sin (y 2- 4x). Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: Use the appropriate form of the chain rule to find the derivatives. w = 12x2 + 12y² + z²; x= p sin o…

A:

Q: Consider y3-2x2=1+sin(xy)   a) Use implicit differentiation to find dy/dx.   b) Find an equation…

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Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

Q: 2. Find y' by implicit differentiation. (5) xy =1+ xy

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Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

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Q: 1. Find the differentiation of the following functions with respect to x I. y = Jx3 + 5x – 7) II. y…

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Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: 2. Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ = x + y = 0 (b) x…

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Q: Suppose that x and y are related by the given equation and use implicit differentiation to determine…

A: →duvdx = udvdx + vdudx→dkdx = 0  where, 'k' is any constant.

Q: 4- Find dy/dx for y = 3[(sin-"(e-3x*)²

A: f(x) = 3arcsin2e-3x2f'(x) =ddx 3arcsin2e-3x2=ln(3)·…

Q: 1. Find dy/dx by implicit differentiation.  x sin(y) + y sin(x) = 7  y' = ?

A: Note:We are authorized to answer one question at a time, since you have not mentioned which question…

Q: Find dy/dx by implicit differentiation and isolate dy/dx: 16. xy = sqrt{x^2+y^2}

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Q: 1. Find the derivative of the following functions (dy/dx) at x=Tt/4 cos x2 1– sin x2 y= 2. Find the…

A: We have to find the derivatives of given function at x=π/4  1. y= cosx2/(1-sinx2) 2. y=x3sin3xcos3x

Q: 1. b. Find the differentiation of the following functions: i. y = 2 tan(1 – 2x) + e*²+x ii. y =…

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Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: 6. Let y + xy - y = 8x*. a) Find dy/dx using implicit differentiation. b) Find the equation of the…

A: In implicit differentiation, when we differentiate y, we use dy/dx

Q: Can you help me with this problem step by step?

A: Given:

Q: Let y=(x to the 2nd power +3) to the 2nd power . Find the differential dy when x=4 and dx=0.2…

A: Given,    y=(x2+3)2

Q: Find the derivative of y: 1- y = (cos 0)▼2

A: See the details solution in below

Q: Use the appropriate form of the chain rule to find the derivatives. 5.x2 + 5y2 + z²; x psin ф сos 0,…

A:

Q: Solve for the derivative of the given implicit functions. a. Find dy/dx for y= ln (4x+tan-1(lnx)).…

A: Solve: a. Find dy/dx for y= ln (4x+tan-1(lnx)). b. Find dy/dx for y= tan-1 (3x-2 sinx). c. Find the…

Q: 4. a) Find the following derivatives using differentiation rules. d dx 5 2)* d ii) Vx + dx d²y b) If…

A: 4 First we will see differentiation rules.…

Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: 14. Consider the curve defined by x2y2 - 3x2 - 6y2 0. dy a. Use implicit differentiation to find :…

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Q: 9. Find dy/dx using implicit differentiation, °y- xy = 4 |

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Q: dw of w==+ dt x. y Use the chain rule to find the derivative with x = cos 1, y = sin ?t, z = - dw…

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Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

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Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: 21. Find y' using implicit differentiation. a) In (xy + x + y) = 2 b) In (sin xy) = xy

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Q: 1. Differentiate the function f(x) = (4x – 5)*(3x – 1)ª %3D d²y for y = 2x sin 5x dx? 2. Find dy…

A: It is derivative problem.