y' = x2y2/x2+y2 ; is this function seperable or non-seperable

Q: 9. State the Second Derivative Test for functions of two variables z = f(x, y)

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Q: Find the first derivative of the function y = 2ArcsinV(x/2) %3D

A: Consider the given function, y=2Arcsinx2 It also can be written as, y=2Arcsinx2=2sin-1x2

Q: Find the derivatives of the functions in Exercis y = xe-x + ex3

A: y=xe-x+ex3

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

A: Given       f(x)=2sin x

Q: ind y' by implicit differentiation: xy3 - sqrt (x2 +1)=2y

A: Definition used -    Implicit differentiation-  If equations do not define explicitly y as a…

Q: Find the derivative using the long method y = vx + 2

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Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

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Q: Solve for the derivative of the Hyperbolic Differentiation. 1. y = ex cos h 2x 2. y = ln sin h x…

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Q: 2. Determine the second derivative of f(x)= x'e* at x = -2 with a step-size of h=0.50 using Central…

A: Given function is f(x) = x2e2x and h = 0.50

Q: Find  y ″  by implicit differentiation. 2x3 − 5y3 = 5

A: We will differentiate w.r.t x twice using the product rule and the chain rule

Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: Find the derivative of the function. y = 3x + V3 3x + V3x y' =

A:

Q: y=9 arctan (x+sqrt(1+x^2) )

A: ddx(xn)=nxn-1 ddxx =12x ddxtan-1(x)=1x2+1 Chain Rule: if f=f(u) where u is a function of x then…

Q: find y' by implicit differentiation. ex/y=3x-2y

A: To find the derivative of the equation using implicit differentiation.

Q: Find the derivative of the function y =2cosx – 3sin x +1

A: Given, y=2cosx-3sinx+1

Q: The total derivative of f(x,y) = ylnx  is

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Q: Obtain the derivative of the function y 4y sen (3x) – 7x In(2x + y) = e* - ey + 4tg(y)

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Q: 1 F(x) = -1. tanh 3x

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Q: Find the derivative of the function. y = ek tan(V 5x) y'(x)

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Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

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Q: Determine the derivative of y=(x−1)4 without using the power rule.

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Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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Q: Find the derivative of the function. y = 3 tan(x - V1 + x 1 + x2 y' = ||

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Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

Q: Find the derivative of the function y= arctan x +x/1+x2

A:

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: 2. Determine the second derivative of f(x) = x²e²* at x = -2 with a step-size of h=0.50 using…

A: Given function f(x)=x2e2x. The objective is to determine the second derivative of fx at x=-2 with a…

Q: Why does the maximum and minimum points for y = f (x) occur among the minimum and maximum points for…

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Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) %3D f (x) =

A:

Q: Find y''by implicit differentiation. 2x3 + 5y3 = 2

A: We can find y" using implicit differentiation as below.

Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: Find the derivative of the function y = 2x − cosh √x

A: The given function is y=2x-cosh x. Obtain the derivative of y=2x-cosh x as follows.

Q: 9. For f(x) = arctan (2 sin ( Vx )) , compute the first derivative at the point %3D X =

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Q: Differentiate the function (x + y)1/2 = x4 + y4 by implicit differentiation.

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Q: nd the derivative by the limit process (Gener x) = Vx2 - 4

A: In this question, the concept of the derivative is applied. Derivative The derivative is used to…

Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: Find the first and second derivatives of the function. f(x) = x/(7+x2) Identify the intervals on…

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Q: Draw the function x = 2y-y2 by using the tools of derivatives?

A: The given function isx=2y-y2.

Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

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Q: 2. Determine the second derivative of f (x)=xe* at x = -2 with a step-size of h=0.50 using Central…

A: Given f(x) = x2e2x

Q: If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f…

A:

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

A: The detailed solution is as follows below:

Q: Find the derivative. f(x) = tanh(2 + e4x) f '(x)

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

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Q: If 5x + 2x + xy = 3 and y(3) 16, find y'(3) by implicit - differentiation.

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Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…

Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

A: