Suppose x and y are variable (y is a function of x) that satisfy the equation sin(x+ y) =xy, What is the result for the derivative of y with respect to x? dy cos(x+y)-y A dr x-1 dy cos(x+y)-y B dr x- cos(x+y) dy cos(x+y) -y dr cos(x+y) - x !! dy cos(x+y) -y

Q: 4. Find using derivative rules. dx sinx x8+x x2 tanx (a) y = (b) y= (c) y = cos³(3x² + 9) cos(5 x*)…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

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Q: 13. We know that x = r cos 0 and y = r sin 0, then find the derivative af/ar if 1 f = ? + y?

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Q: 1. (x*+2x)°(6x²+4)dx 2. [3x²+2x+1 dx 3. (x?)/(x³-4) dx 4. (x+1)/(\x²+2x+1) dx

A: As per the guidelines we can solve 3 problems only.

Q: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

A: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

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A: We have to find the directional derivative.

Q: The derivative of the function y = xe(5+sec(2x)) is: y' = [1+ 2x sec(2x) tan(2x)]e(5+see(2x)) y' =…

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Q: Find the derivative. y = 3t cos (t6) dt Select one: 3 A.6x cos (x ) 3 3 B.3 cos (x ) - 3^/x sin (x )…

A: The solution are next step

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y) =xy, What is…

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Q: Find the derivative w = sin* y cos*y a. sin³ 2y cos 2y b. sin² 2y cos 2y c.sin 2y cos 2y d. sin 2y…

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Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

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A: Consider the given information: u2=6u'2=2v2=-3v'2=-4 Consider the given derivative. ddxuvx=2

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A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

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

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Q: If f(x.y)=sin (2x+y) then the derivative f, Is 2 cos (2x+y) a. b. cos (2x+y) c. 2 sin (2x+y) d. 2…

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Q: The third derivative of y = cos 1 sin 27 1 111 a) y" b) y" 27 %3D 3 1 1 c) sin d) y 27 y = - %3D 27…

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Q: Find the derivative of the following functions: = Arccos 4x -4 ans. y' = V1-16x2 4. y = Arcsec(sec…

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Q: Find dy/dx using appropriate derivative rules. 1. y = 8x^5/2 - 7x-9 + square root of 5 2. ) y =…

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

Q: 1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x

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Q: suppose u and v are differentiable functions of x. Use the given values of the functions and their…

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Q: 14. Find the derivative of y = e cosz %3D A. y' = -ecosx sin z B. y' = elinx cos x C. y' = -etinx…

A: Given,y=ecosxdifferentiating both the sides w.r.t. xdydx=ddxecosxUsing chain…

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Q: The derivative of f(x) = ln( is cos x - Select one: O f'(x) = sinx O None of the other options O…

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Q: is The third derivative of y = cos 3 1 sin 27 1 a) y" b) y" =- cos %3D %3D | - 3 27 3

A: The given differential equation is : y=cosx3   -1

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Q: Suppose x and y are variable (y is a function of x) that satisfy the equation sin(x+y) =xy. What is…

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Q: Let f(x) =x-cos(x²). what is the correct result of the derivative of f with respect to x? A f'(x)…

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Q: ind the derivative of y with respect to x. y =-cos-16x + 7° 6 6. 1 + (6x + 7)2 81 - (6x + 7)2 O 4.…

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Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

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Q: Find the third order derivative of y = In(cos(2x))5. %3D A. y' = -40sec² (2x)tan(2x) %3D В. у' 3…

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Q: The derivative of y = In(sin(ex + 1)) is O y' = -ex cot(ex + 1) the above y' = -ex tan(ex + 1)

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Q: 10.Suppose that x and y are related by the equation 5x 2−4y 2=2 and use implicit differentiation…

A: The given equation is 5x2-4y2=2

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: Suppose x and y are variable (y is a function of x) that satisfy the equation sin(x+y) =xy, what is…

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Q: 3. Find the derivative of (a) f(x) = (x+ 4 sin æ) (1 – 6 cos a), an (b) sin r g(x) %3D 6x

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Q: Suppose x and y are variable (y is a function of x) that satisfy the equation sin(x+ y) =xy, What is…

A: Givensin(x+y)=xyTo find the derivative of y with respect to xFormula:(uv)'=uv'+vu'ddx(sin x)=cos x