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### Implicit Differentiation Exercises

Exercises from public domain textbooks. Solutions where provided do not necessary follow the same lines as the original.

Solutions are not given for exercises whose number is not linked

Some exercises which do not have a textbook solutions are worked: beware of errors.

#### Implicit Differentiation Exercises

Find dx/dy implicitly and solve for y and differentiate explicitly:

#### C25-9 {$x^3 + y^2 - 3x = 0$}

C25-10

{$$(x + y)^3 - 2x = 4$$}

C25-11

{$$xy^2 - x^2 + y^2 - 0$$}

Find dx/dy implicitly. When possible, check by solving for y and differentiating explicitly:

C25-12

{$$x^2 + 2xy + y^2 = 2$$}

C25-13

{$$x^2y^2 -8xy +7 = 0$$}

C25-14 note: d and x in the equation are the variables d and x

{$$ax^2 + 2bxy +cy^2 + 2dx + 2ey +f =0$$}

C25-15

{$$ax^2 + 2hxy + by^2 = k$$}

C25-16

{$$y^4 - 2y^2x + x^2 = 0$$}

C25-17

{$$\sqrt{x} + \sqrt{y} = \sqrt{a}$$}

C25-18

{$$x^{3/2} +y^{3/2} = a^{3/2}$$}

Sources:

1. Elements of the Differential and Integral Calculus Wikisource
2. Calculus Made Easy by Silvanus P. Thompson Project Gutenberg
3. Davis,Ellery Williams, William Charles Brenke, Earle Raymond Hedrick. The Calculus (Macmillan Company, 1922) Google Books
4. Love, Clyde E., Earl David Rainville Differential and Integral Calculus (Macmillian, 1916) Google Books

Recommended:

Category: Math Calculus Implicit Differentiation

This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

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### August 05, 2017

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