Exexcises E Set 2] Implicit Differentia tion x=x 2. Find dy if dX 1. +Sin xy Find dy if 2x²- 3y'=8 2- 3- Use implicit differentiation to find dy A- xy- Cot (xy) B.

Q: Find dy/dx by implicit differentiation. y sin(x?) = -x sin(v?) = -x sin y- y' = %3D

A: ysin(x2)=-xsin(y2)

Q: dy by implicit differentiation. dx Find cos(x + y) = sin(x) + sin(y) dy dx

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Q: dy using implicit differentiation. dx 3. Find sec (xy?) = (cosh )(tanh a+/Ð) + 2 csc-' (tan(y + 1))

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Q: The slope of the tangent line to the curve at the point where x = O +1 -1 DNE f(x) = sin² x cos²x

A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: 14. S 5 sin 3x cos 3x dx 15. ſ tan? Ode

A: We can solve the given integral as follows:

Q: Find the derivative. sin 0 d. 1 dx 1- x2 de A. tan 0 B. sec 0 C. cot0 O D. cos 0

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Q: Find the second derivative of ƒ (z) = 6 sin (5z). Enclose arguments of functions in parentheses. For…

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Q: Use differentials (or equivalently, a linear approximation) to approximate sin(40°) as follows: Let…

A: Given, f(x)=y= sin 40° Therefore, f'(x)= y'= dy/dx= d(sin 40°)/dx f'(x)= cos 40°

Q: 2. (a) Find the tangent line approximation to sin(x) near r 0. (b) Is the tangent line approximation…

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Q: 6. Find the values of 0 in [0,27) where the tangent line of r = 2 + 2 sin e is horizontal or…

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Q: dy Use implicit differentiation to determine dz given the equation zy + cos(z) = e".

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Q: dy using implicit differentiation. dx tan x = ex + ev. Find y2 Suppose that

A: The given implicit equation is: tanxy2=ex+ey To find its dydx, differentiate on both sides of the…

Q: dy Find for following function by using implicit differentiation. dx 29 + 5e*= sec(2x +1) 3x a) b)…

A: Given1)2y3x+5ex=sec(2x+1)2)sin3(2y)+7=exln(cosy)To finddydx.

Q: Find dy/dx by implicit differentiation. (sin Tx + cos ny)3 = 58 dy/dx = Need Help? Read It

A: Find your answer below

Q: Find the slope of the tangent line to the sine function at the origin, (a) y = sin(4x) 15 y'(0) = 4…

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Q: dy Use implicit differentiation to find dx xª + cos y = x³y5 3.

A: Given : x4 + cosy = x3y5

Q: dy by implicit differentiation. dx 2. Find cos(x) sin(y) = x² – 4y -

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Q: dz Find dz and by implicit differentiation, and confirm that the ду results obtained agree with…

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Q: dy Find using implicit differentiation. dx Hint: First clear the denominator to get 8x² + 6y =…

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Q: 3. It is given that sin(x) + cos(x) tan(y) = 1. Use implicit differentiation to find d dy dx

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Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

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Q: dy Use implicit differentiation to determine dx given the equation a · ev + cos(x) = y². dy

A: We will do implicit differentiation.

Q: a)  Use the hyperbolic identity sech^2(x)  = 1 - tanh^2(x)  to solve 4tanh^2 (x)  + sech^2(x)  =3…

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Q: | cos (nt)sin(at) dt Find

A: This integral can be solved by the method of substitution.

Q: dy Find by implicit differentiation. dz 3+ 5z = sin(ry) dy

A: We can find the answer using implicit differentiation as below.

Q: If x cos' 0 y = sin' 0 dy • the derivative dx and %3D (A) tan' 0 (B) -cot 0 (C) cot 0 (D) -tan e (E)…

A: Given: x=cos3θ and y=sin3θ To find: The derivative dydx

Q: (4) (a) Find dv/dx by implicit differentiation: cot y = x – y (b) Use implicit differentiation to…

A: Take derivative with respect to x and express dy/dx in terms of x & y.

Q: Find by implicit differentiation. 3+ 6z = sin(zy') dy Answer: dz

A: Solution is in step 2

Q: ind y' by direct differentiation (with respect to x).  y = 99cos(x) and    y = 7x sec(x)

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Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

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Q: 6. In(x*y?) %3D х* +уз 7. У- Arccos(e2x)

A: Given In(x3y2)=x2+y3y=cos-1(e2x)we need to find the second derivative of the given equation

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: dy Using implicit differentiation find at the point (0,1) for dx ysinx + xy3 = 5

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Q: dy Use implicit differentiation to find dx sinh(x+ y)= cosh 2x+e?y+1 3.

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Q: dy Use implicit differentiation to find dx 4 3 x'+y = 3x+ 6y` dy dx (Type an exact answer, using…

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Q: dy by implicit differentiation. Find dr 6 + 4x = sin(xy?) dy Answer: dx

A: We have to find the derivative of given function by implicit differentiation. Please see the…

Q: 오. x5 - y3 = 0, (1, 1) dy dr 2. At (1, 1): y' =

A: The given equation is  x5 - y3 = 0.... (1) To find dy/dx

Q: Find the second derivative of f (z) = 6 sin (4z). %3D Enclose arguments of functions in parentheses.…

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Q: dz Find and by implicit differentiation, and confirm that the he results obtained agree with those…

A: Given that fx,y,z=yex-6 sin 2z-2z and find ∂z∂x,∂z∂y by using ∂z∂x=-∂f∂x∂f∂z,∂z∂y=-∂f∂y∂f∂z.

Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 2 = 1

A: Differentiate wrt x

Q: dy using implicit differentiation. dx 3. Find sec (xy?) = (cosh x) (tanh 2+v9) + 2 csc-1 (tan(y +…

A: Implicit differentiation

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: Evaluate: ∫x2-1dx

Q: FIND dy/dx FOR EACH FUNCTION. 1. y = (tanx + sinx)-3

A: 1). Given y=tanx+sinx-3. To find: dydx Solution: Power rule of differentiation states that:…

Q: 16. S(3 sin 0 + 5 cos 0)d0

A: A detailed solution is given below     ( As per our guidelines, i have to answer only 1st question…

Q: 16. Use Implicit Differentiation to find an expression for dy/dx given r*y² + cos(y) = 1. %3D

A: Given: x3y2+cosy=1   We know that; The Sum rule: f±g'=f'±g' The Product rule: f·g'=f'·g+f·g' The…

Q: az dz and ду in terms of r, y, and z. Calculate using implicit differentiation. Leave your answers…

A: Given relation is,  x4+zsin(xyz)=0

Q: 3-Use implicit differentiation to find dy 2 B. xx-Cot (xy) y Sin(. ) = L-Xy

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Q: Assume that y=sin^-1x is a differentiable function of x. By differentiating the equation x=siny…

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Q: Find dy/dx by implicit differentiation. 72 – 5y? = 4 dy/dx = Need Help? Read It

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: