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# Differentiation of Algebraic Functions

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THE DIFFERENTIATION OF ALGEBRAIC FUNCTIONS

Use implicit differentiation to find the dy/dx:
3xy + x2y2 = 1

xy1/2 - 2x + y = 8

(x + y)3 = x3 + y3

3y2 + 5x2 -2x = 5

y4 = x3y2 + x2y3 - 3

Find the indicated higher order derivative of the following functions:

1. Find the 2nd derivative of f(x) = 7x^5 - 4x^3 - 2x^2 - 5
2. Find the 6th derivative of f(x) = 2x^5 - 3x^3 + 4x^2 + 2x - 3
3. Find the 1st and 2nd derivative of f(x) = sqrt(x^2+1)

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#### Solution Preview

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THE DIFFERENTIATION OF ALGEBRAIC FUNCTIONS
Use implicit differentiation to find the dy/dx:
1. 3xy + x2y2 = 1

2. xy1/2 - 2x + y = 8

3. (x + y)3 = x3 + y3

4. 3y2 + 5x2 -2x = 5

5. y4 = x3y2 + x2y3 - 3
(1) 3[x(dy/dx) + y] + 2xy[x(dy/dx) + y] = 0
3x(dy/dx) + 3y + 2x^2 y(dy/dx) + 2xy^2 = 0
(3x + 2x^2 y)(dy/dx) = -3y - 2xy^2
dy/dx = (-3y - ...

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in this solution for differentiating algebraic functions. It helps find the indicated higher order derivative of functions

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