Find the derivative of the function f (x, y, z) = * ++ at the point (-8, 8,-8) in the direction in which the function decreases most rapidly. -V3 4. -3/3 8. -3/2 8.

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

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Q: The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled…

A: Given: Nx=0.03x2+0.315x+34.23x is no of years after 2000

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: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

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Q: Find the derivative of f(z) = e2" (3z2- z)

A: Given, f(x)=e2x(3x2-x) Here, when we try to find the derivative of f(x), both chain rule and…

Q: Find the first derivative: y= ln v5x3 –- 2 5, O y = 222 %3D 523-2 O y' = 322 5z3-2 O y' = 622 5z3-2…

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Q: Qol find the derivative of: - f(z) = (2+22²1/2²) ¹/3 14 3) f(²)= (1+2²) ³/2 -3 7 f(z) = (iz-1)³

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Q: 2. If the derivative of an accurately determined function is replaced with a finite difference, how…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

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 the equation of a line tangent to the graph of f (x) = cotx at x = T/4. .Find the derivative…

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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 the function. y = 3x + V3 3x + V3x y' =

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Q: Determine the intervals along the x-axis on which the derivative in Figure is positive.

A: The slope of a tangent line for a function at a point is the value of the first derivative at that…

Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

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Q: Calculate the derivative.

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Find the derivative of the function. Express it using positive exponents only. y…

A: For power 3, use the power rule. Then use the chain rule

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: Find the first derivative: y = In V2r³ – 5 O y =: 22-5 O y = 4z 22-5 O y = 62 22-5 O y =; 2z-5 O y =…

A: Here we have to find the first derivative of         y = ln(2x3-5)1/3

Q: Find the derivatives of the function f(x) from the first principle x*+4

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Q: Find the derivative of the function. 2 + 2

A: To find the derivative of the function, y=rr2+2

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Shows the derivative function of: TC = Q³ + 2Q²  + FC(Q), where TC = Total Cost and FC = Fixed…

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

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Q: The second derivative of a function is equal to 1. If the graph of the function passes through (0,2)…

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Q: Find the derivative of the function. 2 x* + 2 .2 y 2 y' =

A: y = x2+2x2-25we know:ddx xn = nx(n-1)ddx f(g(x)) = f'(g(x)) . g'(x)

Q: Solve for the derivative of t y =2 V3-z Previous

A: This is a basic differentiation problem

Q: Estimate the derivative of the function f (x) = - – 3 at the point x = 3. 3 3 1/5 1/3

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Q: How do I find the derivative of this problem?

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Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: Find the slope of the graph of the function at the given point. y = x-1 y 2.0| 1.5 6 7 1.0 0.5 0.5…

A: See the details solution in below

Q: Find the derivative of the function. f(x) = ex2 + 2

A: We use the chain rule for derivative

Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

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Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

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Q: Find the derivative of the function: (DO NOT SIMPLIFY): 2z f(z)%3D +2 (高)

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Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

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

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Q: Compute central difference approximations for the first derivative of the function, y =[ elnx)2 , at…

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

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Q: Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on  [−2,…

A: To Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on…

Q: Find the derivative of the function. Vs - 3 f(s) = Vs +3 %3D

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Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.) y=…

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Q: y = x-12; (4,) Use the derivative feature of a graphing utility to confirm your results.

A: We will solve the following

Q: Find the derivative of the function at Po in the direction of A. f(xу) 3 - ху- Зу?, Po(-7,0),…

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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…

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Q: The maximum rate of change of the function 1 ----> at the point (1,-2) happens in direction of and…

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Q: Find the derivative of the function. f(z) 0.6z-0.4z2 - 0.8 f' (z) -

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Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

Q: Compute the derivative of the function y using derivative rules. y = (13x4 +5 - 5)³ (Express numbers…

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Q: Find the value of the derivative of the function f (x) = 16 - |x| at the extremum point ( 0, 16)

A: We have to find the value of derivative of the function f(x) = 16 - |x| at the extremum point…