What is the derivative of y = (x2 + 1) e-3 ? O y = (x² +1) (e-3) + xe² - 3 O y = (x² +1) (e*-3) + 2æe* - 3 %3D O y = (e*-3) + 2æe* - 3 %3D O y = (22 +1) (e"-3). + e² - 3

Q: Find the derivative using the chain rule: x(x^2+1)^(-1/2)

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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 derivative of 3 -8 -5 -5 6 -5 1 0 -2 8 -6 -9 1 -3 0 0 0 -2 0 | f(x) = det -1 0 6 -4 ОА. -…

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Q: Use the Chain Rule to express the second derivative off o gin terms of the first and second…

A: Let y=f o g then we have to find the second derivative of y.

Q: 5. Find the first derivative of y = (2x³ – 1)5Vx² – 1 %3D

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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: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

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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: Shows the derivative function of: e3x+5

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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: ind the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)

A: Given function: y=x-12x-x2-arccosx-1

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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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: 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: 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: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

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Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

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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: 9 Derivative of fi») 1x 4 . 5. 1 f) 1x1cosx, fird f'n)

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

A: Stationary points:

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

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Q: e3x _e-3x Y = e3x +e-3x]

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Q: 3. = 2x-y х+3у

A: We will differentiate the given problem with respect to x.

Q: 7. y = 4 e2x, 4th derivative 8. y = -5 e3x^2, 2nd derivative 9. y = 7 In 7x, 2nd derivative

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Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z - 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: (1) What is the chain rule for derivatives? You can write the rule in any way that makes sense to…

A: Explanation:                        The Chain Rule is a formula for computing the derivative of the…

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: 15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x)…

A: Solving

Q: (2x + 3)4 (5x + 1)(x² + 3) y = (3х — 1)3, Find the derivative of the function x3 + 4 A. dy dx (2x+3)…

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Q: 1. 8rd Derivative of fC x) = 4 x³ - 8x5 1

A: We will use just the basic knowledge of differential calculus to answer this question step-wise.

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: 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: What is the second derivative of f(x)=−x4? at the point x=−3 Do not include "f′′(x)=" in your…

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Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

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Q: 3. Find the derivative of h()= 5²°-2z-1 %3D

A: We have to find derivative

Q: the Chain Rule.

A: Given: y=11-x46. Let, u=1-x4 By chain rule, the derivative of y with respect to x is given as,…

Q: Can the  derivative of f(x) be zero in the interval [-1,0]

A: Given, fx = x4+8x+3  f'x = 4x3+3   We have to find the derivative of fx be zero in the interval -1,0…

Q: Can you please help me with derivatives and the power rule? I am struggling with that.

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Q: 11. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? %3D a. -5 b. -6…

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Q: 2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second…

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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: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

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Q: 10.Anti-derivative of y(2y^2-3)^5

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Q: Find the derivative of the function h(x)= ln(5x+1/7x-2)

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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: how do i find the derivative of this but not simplified  y= (x^2+x+6)(x^1/3-2x^1/2+1)

A: To determine the derivative of the function.

Q: find the derivative of the functions : f'(x)=x(2x-9)^3 y'=x^2squared root of 25-x^2…

A: We have to calculated the derivative of the given functions.