In this question, the function f is differentiable, and f' (x) = g(x). We don't know exactly what f(x) or g(x) are, so your answers will have f(x) and g(x) in them. Compute the derivatives of the following functions. (a) (x + f(x))2º (b) In(x² f(x)) (c) esia(f(x))

Q: Find the derivative of function.

A: Find the derivative of function. y=(ln|x+1|)4

Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x

A: Given Data: Function: fx=x3+2xlnx The product rule of derivative is, ddxfx·gx=fxddxgx+gxddxfx Use…

Q: 3x-4 1. y = Arctan

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Q: Shows the derivative function of: 2x² + ln x²(2x² + 5x − 1)

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Q: Please provide me with the solution to this problem. Please show the work and try to dumb it down so…

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Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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Q: 1) Find the derivative of y =-+x-1 %3D

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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: Find the derivative of f(x) = 1 at x = 3

A: The given function is: fx=1x Using the formula of derivative i.e., ddxxn=nxn-1

Q: y = In- e 2x+1

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Q: What can we use to find the derivative of a function when it is impossible or difficult to isolate y…

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Q: Calculate the derivative of the following function. 7 y = sin '(cos (3x)) If the Chain Rule only…

A: To find the derivative

Q: 14. f(x) = 2 +3cos x

A: using basic properties and application of derivation we will solve this question.

Q: 11 In(x)sin (x²). Find the first derivative of g(x) (x),6

A: As we know that: The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x The Power law:…

Q: y = (Arccos 3x³)³

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Q: 2х Find the second orfer derivatives of y=Tan" 1-x3

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Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: 8. Find the derivative of the function. y= In(1+x)

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Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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Q: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

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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: 1 Find the function whose derivative is (x+1)-

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Q: 3) Find the first derivative of y=(In x)"

A: According to our guideline 3 subparts of question or the first question can be answered and rest of…

Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

Q: 3/x +1 f(x) = X+2 at x = -1

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Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

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Q: Example 2: by using the definition of the derivative, find dy/dx of the function y = 5x + 8x - 3x +4

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Q: Example 4:- By using the four steps rule, find the derivative of the function f(x) = Vx + 2

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Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does…

A: Given the first derivative is: y'=6x+1x-22

Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: Find the first derivative of the function of f(x) using any method?

A: Given,

Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

A:

Q: 1. Y= 3x -x- 2

A: Find your answer below

Q: Example 2: by using the definition of the derivative, find dy/dx of the function y 5x' + 8x - 3x +4

A: We can use definition of limit In order to solve the given problem.

Q: Calculus 11th Edition - Ron Larson Please assist with the question below. Please show &…

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Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

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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: 4 Find the first derivative of y = In X +

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Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: Find the derivative of the function.   y = In(x)/x9

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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: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

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Q: Find the derivative of the function 3- y = e- sin 3x 4- y csc- (x2 + 1)

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Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does…

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…

Q: Find the second derivative of y=x-1 at x=2

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Q: Find the derivative of y with respect to x. Y=(x^2 ln x)^4

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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.