Differential Calculus
Calculus Contents C
      Properties of continuous functions
         Continuous function definition
         Intermediate value theorem - Bolzano's theorem
         Existence of roots
         Extreme value theorem
         Monotone function
      Differential Calculus - Derivatives and differentials
      The derivative of a function
         Definition of the derivative of a function
      Tangent to a curve
      The equation of the line tangent to the given curve at the given point
         Determining the derivative of a function as the limit of the difference quotient
         The equation of the line tangent to the given curve at the given point example
      Determining the lines tangent to the graph of a function from a point outside the function
         Determining the lines tangent to the graph of a function from a point outside the function example
      The derivative as a function
         The derivative function
         Differentiation, determining (or deriving) derivative of a function
      Derivatives of basic or elementary functions
         Determining the derivative of a function as the limit of the difference quotient
         The derivative of the power function
         The derivative of the linear function
         The derivative of a constant
         The derivative of the sine function
         The derivative of the cosine function
         The derivative of the exponential function
         The derivative of the logarithmic function
      Differentiation rules
         The derivative of the sum or difference of two functions
         The product rule
         A constant times a function rule
         Derivatives of functions examples
         The quotient rule
         The derivative of the tangent function, use of the quotient rule
         The derivative of the cotangent function, use of the quotient rule
         The chain rule
         Differentiation using the chain rule examples
      Table of derivatives of elementary functions
         Differentiation rules
         Table of derivatives
     The chain rule applications
      Implicit differentiation
         Implicit differentiation examples
      Generalized power rule
         Generalized power rule examples
      Logarithmic differentiation
         Logarithmic differentiation examples
      Derivative of a composite exponential function
         Use of the logarithmic differentiation
         Derivatives of composite functions examples
      Derivatives of the hyperbolic functions
         Derivatives of inverse hyperbolic functions
      Derivative of the inverse function
         Derivatives of the inverse trigonometric functions
      Derivative of parametric functions, parametric derivatives
         Derivative of parametric functions example
      Derivative of vector-valued functions
 
 
 
 
 
 
 
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