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  2. Differentiation of trigonometric functions - Wikipedia

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

    All derivatives of circular trigonometric functions can be found from those of sin(x) and cos(x) by means of the quotient rule applied to functions such as tan(x) = sin(x)/cos(x). Knowing these derivatives, the derivatives of the inverse trigonometric functions are found using implicit differentiation.

  3. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.

  4. List of trigonometric identities - Wikipedia

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

    Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.

  5. Quotient rule - Wikipedia

    en.wikipedia.org/wiki/Quotient_rule

    Example 2: Derivative of tangent function. The quotient rule can be used to find the derivative of ⁡ = ⁡ ... To evaluate the derivative in the second term, ...

  6. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

  7. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    The derivative of ′ is the second derivative, denoted as ⁠ ″ ⁠, and the derivative of ″ is the third derivative, denoted as ⁠ ‴ ⁠. By continuing this process, if it exists, the ⁠ n {\displaystyle n} ⁠ th derivative is the derivative of the ⁠ ( n − 1 ) {\displaystyle (n-1)} ⁠ th derivative or the derivative of order ...

  8. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    Illustration of the sine and tangent inequalities. The figure at the right shows a sector of a circle with radius 1. The sector is θ/(2 π) of the whole circle, so its area is θ/2. We assume here that θ < π /2. = = = ⁡ = ⁡

  9. Chain rule - Wikipedia

    en.wikipedia.org/wiki/Chain_rule

    The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way. This variant of the chain rule is not an example of a functor because the two functions being composed are of different types.