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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