Find f', f'', f'" and f (4) for the function. f(x) = x° – 2x + 4x - 4 %3D

Q: Find the differential of the function: y = x In x

A: Solution:Giveny=x ln xTo find the diffferentiationformula:(uv)'=uv'+vu'ddxxn=nxn-1ddxln x=1x

Q: Find dy/dx by implicit differentiation   x2 + xy -y2 =4

A: Differentiate both sides with respect to x. For xy use product rule

Q: Find for implicit function dx x² sin y + 3y3 = e5æ + 5

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Q: Find dy/dx by implicit differentiation. 8x3 + x?y – xy3 = -8x2 y' = 2/3

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Q: What is the average rate of change of y = cos (2x) on the interval [0,π/2]

A: Given f(x)= y=cos (2x) to find the average rate of change over the interval (0,pi/2) average rate of…

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) At the point (, (2n…

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Q: find dy/dx by implicit differentiation.   1. x2 + xy + y2 - 5x = 2    2. 5x^(4/5) + 10y^(6/5)=15

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Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

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Q: find the partial derivative of the function with respectto each variable. ƒ(x, y) = 1/2 ln (x2 + y2)…

A: The given function is fx,y=12lnx2+y2+tan-1yx.

Q: Find dy/dx by implicit differentiation. x2 + y2 = 9

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Q: dy by implicit differentiation: 2x 3x? y + y = 15 Find - dx

A: Take the derivative by concept of power derivative and chain rule of derivative.

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Find dy/dx by implicit differentiation. x4 (x + y) = y2 (3x- y)

A: We have to find the dydx by implicit differentiation: x4x+y=y23x-y Rewriting given equation,…

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

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Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Find the partial derivative dz for the function z = cos(x³ +y²).

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Q: find dy / dx by implicit differentiation.

A: We have to find dydx by implicit differentiation: x5+y5=16 We know the formula of differentiation,…

Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

Q: 4. FIND d²y BY IMPLICIT DIFFERENTIATION: x² + y² = 81 %3D dx2

A: Given: x2+y2=81

Q: 3. f(x,y) tanx - sec²x - cosy

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Q: Find dy/dx by implicit differentiation. x2 + xy - y2 = 4

A: Given function is, x2+xy-y2=4.   It is implicit differentiated as follows:…

Q: Find the derivative of the function. f(x) %3D еx sec(9x) cos (9x) · e* + 7e* · sin(9x) f'(x) C cos…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occur f(x, y)…

A: Topic- Vectro

Q: Compute the derivatives. Use the fact that e2+x = e2 . ex to find d/dx (ex+2).

A: ddxex+2

Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

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Q: y = sinx from x = = to x = n and the x axis 2

A: The required solution is:

Q: Use differentiation rules to find y' = dy/dx.

A: To determine the derivative of the function.

Q: Find dy/yx by implicit differentiation x^3-xy^2+y^2=2

A: Given function is x^3- xy^2 +y^2 = 2.Implicit differentiation is a special case of the chain rule…

Q: Find the derivative. 8) y =V4x +2 dy dxN4x + 2 =N4x + 2 A) dy В) dx 4 1 N4x + 2 dy C) dx dy D) dx 8…

A: SOLUTION-

Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

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Q: Find dy/dx by implicit differentiation. x5 + y5 = 16

A: To Determine: Find dy/dx by implicit differentiation. x5 + y5 = 16 Given: we have x5+y5=16…

Q: Find the indicated derivative. 1 - 2x2 x4 - 2x2 + 4 dy for y dx dy dx %3D

A: We will find dy/dx, using the form of             d/dx (u/v) .

Q: Find dy/dx by implicity differation.

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Q: The average rate of change of the function y = x² in the interval 2 sx< 5 is %3D

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Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: 23-4z2-2一4 y = %3D 1+ Va

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Q: find dy/dx by implicit differentiation x^4+x^2y^2+y^3=5

A: Given: x4+x2y2+y3=5 We have to find the derivative of the given equation. The product rule of…

Q: Find the indicated derivative. 1 - 2x2 x* — 2х2 + 6 dy for y : dx - dy %3D dx

A: Quotient rule of differentiation:…

Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: First find gradient and take magnitude for max rate of change

Q: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

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Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 ; d'y/dx 1. y = 2. Y = (7x + 2)5…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

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Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

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