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  2. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    The following table shows how inverse trigonometric functions may be used to solve equalities involving the six standard trigonometric functions. It is assumed that the given values θ , {\displaystyle \theta ,} r , {\displaystyle r,} s , {\displaystyle s,} x , {\displaystyle x,} and y {\displaystyle y} all lie within appropriate ranges so that ...

  3. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variable. For example, the derivative of the sine function is written sin ′ ( a ) = cos( a ), meaning that the rate of change of sin( x ) at a particular angle x = a is given ...

  4. Template:DomainsImagesAndPrototypesOfTrigAndInverseTrigFunctions

    en.wikipedia.org/wiki/Template:DomainsImagesAnd...

    The table below displays names and domains of the inverse trigonometric functions along with the range of their usual principal values in radians. Name Symbol

  5. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of f {\displaystyle f} is denoted as f − 1 {\displaystyle f^{-1}} , where f − 1 ( y ) = x {\displaystyle f^{-1}(y)=x} if and only if f ...

  6. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    In particular, this explains use of integration by parts to integrate logarithm and inverse trigonometric functions. In fact, if f {\displaystyle f} is a differentiable one-to-one function on an interval, then integration by parts can be used to derive a formula for the integral of f − 1 {\displaystyle f^{-1}} in terms of the integral of f ...

  7. Quotient rule - Wikipedia

    en.wikipedia.org/wiki/Quotient_rule

    In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = (), where both f and g are differentiable and ()

  8. Antiderivative - Wikipedia

    en.wikipedia.org/wiki/Antiderivative

    The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.

  9. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

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