


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 vectorvalued functions 















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