What is g'(x) when g(x) = 1 3z²+6z+7 2z²+2x³

Q: 3. Given the equation y = x³ - 3x² + 3, determine all Critical Points and classify using the SECOND…

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Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: Find the derivative: y = ln² (3x + 1) O y' = O O O y' = y' = y = 2 ln(3x + 1) (3x + 1) 6 (3x + 1) 3…

A: Consider the function y=ln2(3x+1). The objective is to find the derivative of the function.

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

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

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 derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: Find y" by implicit differentiation. 3x3 + 4y3 = 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 the function. y = 3x + V3 3x + V3x y' =

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Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

Q: How to find the critical points of this derivative

A: We have to find critical point of f(x),where f'(x) is given by:

Q: find derivative       1. y = ln 3x + x    2. y = ln (t2)    3. y = ln (3/ x)    4. y = ln (u + 1) -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If 3x2 + 3x + xy = 2 and y(2) 8, find y' (2) by implicit differentiation. %3D 1

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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: 3x V1-x x = 0. y(x) = at Equation of the tangent line

A: Given,           yx=3x1-x2 at x=0

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Find the derivative: y = ln(24) 2x-4 O 4x-x² 2x-4 x²-4x 4 4x-x² 4 x²-4x O о O 8

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

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Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

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

A: We can make it easier for you

Q: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: 2 Find the derivative of: 9/x + 4x – 2 - - d 2 + 4x - - dx II

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Q: What is the value of the first order derivative of the closed function given as…

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Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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

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Q: Find y" by implicit differentiation. 4x3 + 5y3 = 6 У" :

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Q: 2. Find y' by implicit differentiation. (1) xy-3x+2x =8 (2) 9x² +4y² = 25 (3) x²+2xy- y² =5 2 3 = 6…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

A: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

Q: Find the partial derivative. 4 = (x² + 6x – 3y)* - dz

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Q: 5. Find the first derivative of y = (2x³ – 1)5 Vx² – 1

A: Given: y = (2x3 – 1)5√(x2 – 1)

Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.

A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…

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 f(x,y) is a real valued function of two variables then what is the second derivative of f?

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Q: 2. The derivative of y = (1 + Vx3) (x3 -2 V) is y'=-3x4-3xs-2z2-11xº.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 2. Find the derivative of y = (5x³ + 2 x)tanx. %3D

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Q: What is the first derivative of f(æ)= ln(3z²+7z )? 5z

A: Given  f(x)=ln3x2+7x5x We know that derivative of ln(x)=1/x…

Q: Find a function with the given derivative whose graph passes through point P f'(x)=1/x+2, x is…

A: The derivative is given as

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

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: What is the derivative of y (2æ)* O (2x)^(x) (1-2 In2x) O (2x)^(x) (1-In2x) O (2x)^(x) (1+2 In2x) O…

A: Given; y=(2x)x.

Q: 5. Find derivative of the following composite function using the Chain Rule: f(x) = 3x2 + 8x, x(t) =…

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

A: The detailed solution is as follows below:

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: What is the derivative of y = (2x)" O (2x)^(x) (1-In2x) (2x)^(x) (1+2 In2x) (2x)^(x) (1+In2x) O…

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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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