2.6.5. Derivative of implicit function

Lecture

The implicit function y of the argument x is a function whose values are found from the equation linking x, y and not resolved with respect to y , i.e. .

The derivative of an implicit function is found by the following formula: .

The implicit function z of the x and y arguments is a function whose values are found from the equation linking z, x, y and not resolved with respect to z , i.e. .

Derivatives of an implicit function are given by the following formulas:

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Lectures and tutorial on "Mathematical analysis. Differential calculus"

Terms: Mathematical analysis. Differential calculus

Indeterminate form

2.1. Real argument function

2.1. The concept of the limit of function

2.2. Equivalence of infinitesimal

2.3. Unilateral limits

2.4. Bound theorems

2.5. The first and second wonderful limits

3. Continuity of function 2.3.1. Continuous and discontinuous functions

3.2. Break points and their classification

2.4. Derivative 2.4.1. Derivative Definition

4.2. Basic rules for differentiation

4.3. Derivatives Table

4.4. Derivative of a parametrically given function

4.5. Differentiation of exponential-power function

2.5. General investigation of the function 2.5.1. Decreasing and increasing function

5.2. Function asymptotes

5.3. Extremum functions

5.4. Convexity, concavity and inflection points

5.5. Plan a general study of the function

2.6. Functions of many variables (FMP) 2.6.1. Scope of FMP

2.6.2. Partial derivatives

2.6.3. Full differential

2.6.4. Derivative of a complex function

2.6.5. Derivative of implicit function

2.6.6. Extremes FMP

2.6.7. Directional derivative, gradient

Examples of solving problems to the section limits and derivative. differential calculus

Zero to the power of zero