Implicit Differentiation: Finding Derivatives of Given Functions, Summaries of Mathematics

The steps to find the derivatives of the implicit functions x^2 + y = 1, x^2 - 4x - y = 7, and 3x^3 + y^2 = 9 using implicit differentiation. The given functions, the steps to apply implicit differentiation, and the final answers.

Typology: Summaries

2017/2018

Uploaded on 09/24/2022

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Use the implicit differentiation to find the derivatives of
the given functions.
1. x^2 + y = 1
= 2x + y dy/dx = 1
-2x -2x
= y dy/dx = -1x
y y
Final Answer = dy/dx = -x/y
2. x^2 - 4x - y = 7
= 2x – 4x – y dy/dx = 7
-2x -2x
= -4x- y dy/dx = 5x
4x 4x
= y dy/dx = 9x
y y
Final Answer= dy/dx = 9x/y
3. 3x^3 + y^2 = 9
=9x^2 + 2y dy/dx = 9
=18x + 2y dy/dx = 9
pf2

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Use the implicit differentiation to find the derivatives of the given functions.

  1. x^2 + y = 1 = 2x + y dy/dx = 1 -2x -2x = y dy/dx = -1x y y Final Answer = dy/dx = -x/y
  2. x^2 - 4x - y = 7 = 2x – 4x – y dy/dx = 7 -2x -2x = -4x- y dy/dx = 5x 4x 4x = y dy/dx = 9x y y Final Answer= dy/dx = 9x/y
  3. 3x^3 + y^2 = 9 =9x^2 + 2y dy/dx = 9 =18x + 2y dy/dx = 9

-18x -18x =2y dy/dx = -9x 2y 2y Final Answer = dy/dx = -9x/2y