Determine L '{F}. - 1 2. 3s + 4s + 2 F(s) = %3D (s+ 1) (s + 2)

Q: finf dy/dx by implicit differentiation when x^2=(3x+6y)/(3x-6y).

A: The given function is: x2=3x+6y3x-6y

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Use differentials to approximate the value of 52.1. 100+ 5ln5 50+ 6ln5 50+ 5ln5 2 100+ 6ln5 4

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Q: Use forward, backward and centered difference approximations to estimate the first derivative of:…

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Q: 3. (D - 3D? + 4)y = 40cos2x + 6

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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: Find the derivative. 2 - - dy dx - if y(x) = 1 x + 3 dy dx ||

A: This question is based on Chain rule diffrentiation. d/dx{f(x).g(x)} = g(x)d/dx{f(x)} +…

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 80x + 0.9x2 −…

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Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

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Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: Use the chain rule to find the derivative of f(z) = 4(4z5+5z“) i

A: Given : fx = 44x5+5x4-12

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

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Q: Find total differential of function u = x.

A: 6. The given function is u=xyz. We know that the total differential of a function u=fx,y,z is given…

Q: what is the partial derivative of 2=Yytylnlxy

A: Given query is to find the partial derivatives.

Q: How would you find the stationary points of partial derivative equations coming from a multivariate…

A: Stationary points:

Q: Find the fourth derivative of ƒ (z) = 4z" f(4) (z) =

A: We can make it easier for you

Q: can explain for me what is Applications of Partial Derivative ?

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Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: Find the average rate of change of the function from x, to x,. Function x-Values f(x) = x² – 3x + 8…

A: The given function and x -values are: fx=x2-3x+8, x1=1, x2=5 Now, calculate the average rate of…

Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let the length of a diagonal is = d1=x m So the length of the other diagonal = d2=(x+2) m. Given…

Q: Find both first partial derivative Z = 15x x/y az az ду

A: As we know that: The the Power law: ddxxn=nxn-1 From the given problem: z=15xy

Q: 3. Tak-gu baked 10 loaves of bread in 1 hour. After that, he baked a dozen of bread in 80 minutes…

A: We have three points,  A = (60 min, 10 )  B = (80 min, 12 )  C = (90 min, 12)    Hence, we have…

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

A: Rate of change.

Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

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Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: What is the equation of the normal line of f(x) = ln(x² – 3) at the point x = 2 ? %3D

A: Given:fx=lnx2-3  at a point x=2

Q: What is the difference of antidifferentiation and anti-derivative?

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Q: Estimate approximate derivative of f(x) = x2 at x = 1, for h = 0.2, 0.2, 0.05, 0.01 using first…

A: Given function is fx=x2. We have to estimate approximate derivative of the given function at x=1 for…

Q: What

A: The correct option is (B).

Q: Find the first and second order derivative w=3z7-7z3+21z2

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Q: Four positive numbers, each less than 130, are rounded to the first decimal place and then…

A: Let p,q,r,s be the four positive numbers and their product be w

Q: Use differentials to approximate the value of s2.1. O 100+6ln5 4 O 50+5ln5 2. O 100+5ln5 4. O…

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Q: Find the indicated partial derivative.

A: Given that, f(x, y) = y sin-1 (x, y) We have to find fy(1, 1/2).

Q: Find the average rate of change of LaTeX: f\left(x\right)\:=3x^2+1 f ( x ) = 3 x 2 + 1 between…

A: Formula for average rate of change is f(b)-f(a)b-a.

Q: Four positive numbers, each less than 80, are rounded to the first decimal place and then multiplied…

A: Solve the given problem.

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

Q: ind the 9th derivative of f(z)=exp((-1 + isqrt 3)z) at z=0.

A: Given f(z)=e(-1+3)z Differentiating w.r.t 'z' f'(z)=e(-1+3)z(-1+i3) f''(z)=e(-1+3)z(-1+i3)2…

Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: Calculate Calculate 1 f (425 - / +6²-8) dz 4x - dx. X S 5² - -x³√x² + 3 dx 3 ln³ Calculate 41³ (2)…

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Q: Q Find the derivative us ing the de fini tion 2. O fcx) Fcx) x+2X %3D

A: Derivative of the function using definition

Q: Use linear approximation or differentials to estimate v80. Show your work.

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Q: What are the real-life applications of antidifferentiation or integrat

A: What are the real-life applications of anti-differentiation or integration?

Q: From a numerical perspective integration is better conditioned than differentiation.

A: As given, We have to state that whether the below statement is true or false. From a numerical…

Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let d1, d2 be the diagnols of a parallelogram given,  d1+d2=18d1=2+d2 ⇒d1=10, d2=8 Area of the…

Q: A curve y = /(x) have length of the curve from x 0 to x= n/2. dy Vcos(2x - 2) as its first…

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