Give a discussion as to why differentiation and integration are inverse processes. You should include clear diagrams where necessary.

Q: 3) Use logarithmic differentiation to find the derivative of the function a) y = Vxe&*x? + 1)"

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Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

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Q: By using first principle of differentiation find f'(y), if ƒ(y) = Му—N

A: Given: f(y)= My-N According to the first principle of differentiation, the derivative of a function…

Q: When is it necessary to use implicit differentiation?

A: To explain: The necessity to use implicit differentiation: Explanation: Implicit differentiation: If…

Q: 4х — бу? 3 ху?

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Q: ן +אק Y= x

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Q: Use logarithmic differentiation to find the derivative of y. 3 (4x + 1)(x + %3D 3)2 V x+ 5)(x + 8)

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Q: Find using logarithmic differentiation if y = (2z). dr %3D

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Q: Find y' by implicit differentiation. 1) x²y° = 2

A: Given equation: x2y9=2 To find: y' by implicit differentiation.

Q: What’s the difference between differential and inferential Calculus? And How do they apply to…

A: DIFFERENCE BETWEEN INFERENTIAL AND DIFFERENTIAL CALCULUS:…

Q: =) Give a discussion as to why differentiation and integration are inverse processes. You should…

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Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" :

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Q: to***) dx . Refresh your integrating skills and evaluate

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Q: On what instance does the Chain Rule of differentiation applicable? Explain briefly

A: To explain when we should use chain rule.

Q: Find xp by implicit differentiation. S 4e*"y = 2x

A: According to the given information, it is required to find the implicit differentiation.

Q: 4. Describes the various ways in which integration and differentiation may be viewed as inverse…

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Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" =

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Q: ) 1 = x* + 5y³

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Q: 4. Use logarithmic differentiation to find the derivative of the function y = x c0sx.

A: So we are going to take natural logrithm to both side and solve them so I'm providing hand written…

Q: What is meant by Implicit Differentiation?

A: In implicit differentiation, we differentiate each side of an equation with two variables by…

Q: What are the formulas for differentiation and integration? How are they applied?

A: To write: Formulas for differentiation and integration.

Q: Use logarithmic differentiation to find the derivative of y. 24) y = Vx(x + 3) %3D

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Q: Use log differentiation to find derivative of y with respect to the given independent variable

A: Topic = Derivative

Q: Use implicit differentiation to find the 2nd derivative of x2 y + y2 x=-2

A: By using implicit differentiation to find the 2nd derivative of x2y+y2x=-2.

Q: First of all, what is the difference between implicit and explicit? How does it apply to our…

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Q: What are the formulas for differentiation and integration? How to apply those formulas?

A: See the attachment

Q: Determine whether the following statement is true or false, and explain why. The chain rule is used…

A: Given: The chain rule is used to take the derivative of a product of functions.

Q: Differentiate by using implicit differentiation x2y+xy2=6

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Q: Find y" by implicit differentiation.   x4 + y4 =a4

A: Given function is Differentiating both sides  with respect to x, we get

Q: What is the derivative of y = e3 In(5 + e3)? %3D

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Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

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Q: What is the derivative of y = ekx?

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Q: 1. y, x= 1+ 1+y

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Q: 4х — бу? %3D ху?

A: Find y' by implicit differentiation.

Q: Q2) Use implicit differentiation to find y'" if y2 – 2x = 1 – y

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Q: Explain briefly how we can compute the derivative of a function y=f(x) using logarithmic…

A: Logarithmic differentiation is an important method of differentiation. To find the derivative of the…

Q: Explain in words and express mathematically the inverse relationshipbetween differentiation and…

A: We need to Explain and express mathematical relationship between the differentiation and integration…

Q: Explain how to find a differential of a function.

A: Let us consider a function f(x) and its differential to be f'(x)

Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

Q: What is the inverse process of determining a function whose derivative is known?

A: The inverse process of determining a function whose derivative is known is called

Q: Discuss how the processes of integration and differentiation can be considered as “inverses” of each…

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Q: Find y" by implicit differentiation. 4x3 + 5y3 = 1 y" =

A: We will find the y" of the given function using the implicit differentiation.Below find the solution…

Q: Using logarithmic differentiation, Show that y (x)= xa2" e®has no stationary points other than x =…

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Q: How do we know when to use implicit differentiation?

A: Implicit differentiation is the procedure of differentiating an implicit equation with respect to…

Q: 19. Determine the derivative of f(x) = e* coshx. O a. e2x O b. ex O c. e4x O d. e5x

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Q: Find the first derivative of f = (h+2)² (2h+1) h²+3 V using logarithmic differentiation

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Q: Which order of differentiation will calculate fxy faster: x first or y first?  a. ƒ(x, y) = 1/x b.…

A: Consider ƒ(x, y) = 1/x

Q: w(x) %3D хе*

A: To find the second derivative of function w(x)=xex

Q: 1= x* + 5y3

A: The given equation is 1=x4+5y3

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan x V…

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