Find y\\ for each of the following functions: 1- f(x)=sin(xe). 2- f(y) = sin (3y)+ e-2y + In (7y)

Q: find the derivatives y=sin^3(x)+sin(x^3))

A: we have to find the derivative

Q: Find y" by implicit differentiation. x² + 5y2 = 5 %3D

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Q: Assume that y = sin'x is a differentiable function of x. By differentiating the equation x= sin y…

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Q: B) Findfor the Implicit function: dx x² - sin(xy) + y² = 5xy

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Q: Find y" by implicit differentiation. x² + 4y² = 4

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Q: Find the value of the derivative (if it exists) at each indicated extremum.           f(x) = cos x/2

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Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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Q: Find y" by implicit differentiation. x² + 6y2 = 6 -2 12 y" =

A: Topic -double derivative using implicit differentiation

Q: Find y" by implicit differentiation. x2 + 9y2 = 9 y" =

A: Here we have to find the both y' and y"

Q: Let y be defined implicitly by the equation 2x° + 5y- 4x – 7y = -2. dy at the point (1,0). dx Use…

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

A: GIVEN dy /dx.(x + 1)2 (y - 1)2 = 1 We need to find the  differentiation

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: 2. Calculate the derivative of the following. А. y = (x* – 3x² + 5x) ³ DUKAS B. y = tan²(x² + 5x –…

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Q: Consider the function f(x) whose second derivative is f′′(x) = 18x + 3 cos x. If f(0) = 4 and f′(0)…

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Q: Find the derivatives of the functions y = (3 + cos3 3x)-1/3

A: Given that, y=3+cos33x-13

Q: Find the derivative of the function. f(x): f(x) = 2xarccos(x) – 2/1 – x² 2arccos(x) + 2 2arc cos (x)…

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

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

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

A: Suppose that x and y are related by thegiven equationx5y+y5x=9we have to find dydx

Q: for (e3x+y2)5 = sin x cos y, find dy/dx. using implicit differentiation. must show all steps

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

A: Given equation x3+y3=x3y3

Q: Find the second order derivatives of the function f(x) ex sinx cos 2x

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Q: Find the derivative of each function: 2x+3 y = Зх +2 а. b. y =x sin 2x tan x c. y = e" d. x² +xy+ y…

A: we have to find the derivative of each of function

Q: Find the derivatives of the function defined as follows.

A: Consider the given function y=cos xcos 4x   Apply the chain rule: ddxy=ddxcos xcos 4xy'=12cos xcos…

Q: Find the derivative of the given functions. 1. D;(x²cos 2x) 1 1 2. y =x + 7sin 2x 3. f(x) = sin?(5x…

A: We have to find

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

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: Match each function with its derivative. Y • x² x4 + 5x 1. cos x - - x8 8. sin x + x4 3x x4 -1.…

A: Concept: Differentiation of xm dydx=xm=mxm-1 dydx=ax=loge(a)· ax

Q: Find the derivatives of the functions defined as y = cos (4e2x)

A: Given information: The function is y=cos4e2x. Concept used: Chain rule of…

Q: Find the derivatives of the function defined as follows. y = -3e2sin x

A: The function: y=-3 e2 sin x

Q: Find y" by implicit differentiation x2 5y2 5 + = 2 X у"-

A: Take d/dx on both sides and distribute it on the left side. Derivative of constant =0

Q: Find the derivatives of the function defined as follows.

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Q: Find the derivatives of the functions in Exercis

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Q: by implicit differentiation if x² +9x+9xy-y² =16 Find x dy

A: Find dydx by implicit differentiation if x2+9x+9xy-y2=16. Solution: Power rule of differentiation…

Q: r (4x2 – 3x + 5)* - 3.) c(x) = %3D sin x

A: solution:- find the derivative by using the quotient rule

Q: Find an equation of the line tangent to graph of y =x2 + sin (Ex) at x=-1. A. 2x - y+2 = 0 B. 2x +…

A: To find the equation of tangent line of the given graph.

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: Determine the derivative of the following functions. 1. y = 9x cos(2x + 3) 2. y = cos(x + y)

A: According to the question, we need to calculate the derivative of the given function.    Function 1:…

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

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

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Q: Find by implicit differentiation. dx 1. x3 – xy + y? = 7 2. x³y + y?x = -3 3. xy = x?y + 1

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Q: Find 0ƒ/0y as a function if ƒ(x, y) = y sin xy.

A: fx, y=ysinxy

Q: Find the derivatives of the functions y = 3/(5x2 + sin 2x)3/2

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Q: Find y' by implicit differentiation: a.) 2y3 + 4x2 - y = x6 b.) ex - sin (y) = x

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Q: Find the derivative of y Cos3 3x+8 (x). %3D Provide your answer below: y = D

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Q: Find the derivatives of the functions y = x2 sin2 (2x2)

A: Given that : The function is y = x2 sin2 ( 2x2 ) .

Q: Determine the derivative of y=tan(cos-'(4x)) -1 A y'= 4x2/1- 16x2 - 4x B y'= V1- 16x2 c) None of the…

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Q: 2- find dy/dx e2x = sin (x + 4y) 3-find an equation for the line tangent to the graph f(x) = x –…

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Q: Find the derivatives of the functions defined as follows.y = -4 cos(7x2 - 4)

A: The given function is, y=-4cos7x2-4 If a function is the function of some other function as y=fgx,…

Q: Find the slope of the graph of cos(x + y) = 2x at the point ( 0, T1/2 ). Hint: Differentiate…

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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: