8) Use implicit differentiation to find y', given cos(x+ y) = y² sin x

Q: In xy = x² + sin xy

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Q: Find y’ if y=cos(ln(x^2 +1)) y’(0)= Use implicit differentiation to find the equation of the tangent…

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Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

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Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: 4. Find by implicit differentiation of x sin(y) = y cos (x) dx

A: The given problem is solved below in detail.

Q: 6. Find dy/dx by implicit differentiation for tan-'(²y) = sin(x²) + 3ry?.

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Q: Find the first derivative x2y + y2-2xy =5                   Use implicit differentiation

A: The given equation is x2y+y2-2xy=5. Assume y is a function of x. By implicit differentiation, find…

Q: Suppose that x and y are related by the equation 2x-y 2 and use implicit differentiation to…

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Q: Find y" by implicit differentiation. cos(y) + sin(x) = 1 %3D

A: Chain rule:- if f and g are both differentiable and F(x) is a composite function defined by…

Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

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Q: Use chain rule of differentiation to find  Y is equal to 3x²-5x +12 X is equal to 2u²-5u +11 Find…

A: Consider the given function asy=3x2-5x+12 And x=2u2-5u+11

Q: Find y' by direct differentiation (with respect to x). y = 10etan(x) and y = (x3 + 4) sin(x)

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Q: Find by implicit differentiation for x2+y2=25 at point P(0,5).

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Q: Find the derivative of cos (ry) = -4x° y? + 5 using implicit differentiation.

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Q: Q2) Apply the differentiation rules to find the derivatives of: Inx 5 (a) y=x*.e*+2- Inx- cosx (b)…

A: Solve the following

Q: Q1) Use implicit differentiation to find dy/dx if x cos(3x + 2y) = y sin x

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Q: 4. Use implicit differentiation to find an equation for the tangent line to the graph of sin(x +y) =…

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Q: 7. Use implicit differentiation to find an equation for the line tangent to the curve 2² + 2xy – y³…

A: Given :           x2+2xy-y3=0

Q: 17. Find the first derivative for J(x)=tan0x sec0

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Q: Find the derivative of y with respect to x. -1 2х + 3 26) y = sec" 27) y = -sin-1 (5x2 + 2) 28) y =…

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Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Part 1 : Slope of tangent at (π2, π4) is given by dydx(π2, π4) ⇒y·sin 8x=x·cos 2x⇒ddx(y·sin…

Q: Find the derivatives of the functions y = x2 sin4 x + x cos-2 x

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Q: (6) Use implicit differentiation to get y`, where + cosh y = e*".

A: Explanation of the answer is as follows

Q: Find y' by implicit differentiation. cos(x) + √y = 2 y' =

A: Explanation and solution is given below....

Q: 19. y = sin-1+ cos-1 2 2

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Q: Find the 3rd derivative of (1 + 2y)³ + eª (sin² y) - 3y cos(e=? )

A: Given data (1+2y)3+ex(sin2y-ycosex2=3y and find 3rd derivative or d3dx3=?

Q: Find y" by implicit differentiation. 2 + 6y = 6 y"

A: Here is the solution

Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

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Q: 4. Find the derivative of the following function. 1+ sinx g(x) = - V1+ cos x

A: Given: gx=1+sinx1+cosx for finding derivative of given function, first we simplify given expression…

Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: Question 7

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Q: Compute for y" by implicit differentiation. sin y + cos x 1

A: This question is based on diffrentiation of implicit function.

Q: Find the derivative of y = 2x cos x − 2 sin x.

A: Given function y=2xcosx-2sinx dydx=ddx2xcosx-2sinx=ddx2xcosx-ddx2sinx Recall the formula…

Q: Find the derivative of y = csc¯(In sin (x))

A: use simple integration formula.

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

A: we are given the function is  f(x)=1+sin2x2cos3x

Q: Find y' by implicit differentiation: 8 cos(ry) + x4 = yª

A: Given: 8cosxy+x4=y4 For finding derivative of given expression, we differentiate given expression…

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

Q: Find the first derivatives of y = cos x tanx

A: Given: y=4cos x+1tan x

Q: Find the second derivative, y" for the function cos(y) + sin(x) =1 by implicit differentiation. %3D

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Q: by implicit differentiation. 8. Find dx sin(xy) = 1+ cosy,

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Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

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Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: 5. Find the derivative of --( 1 + sin 0 cos 0

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Q: 31. Differentiate x+3xy2: =1- cos y using implicit differentiation. [Value of 3]

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Q: 3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x

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

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Q: 1. Find by implicit differentiation for xe = 2xy + y³.

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Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x

Q: 5. Find dy/dx using implicit differentiation given x²y³ + cos y = 0.

A: Definition used -  Implicit differentiation -     It is a rule by which we can find the derivative…