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  2. Differentiation of trigonometric functions - Wikipedia

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

    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 by the cosine of that angle. 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 ...

  3. Arctangent series - Wikipedia

    en.wikipedia.org/wiki/Arctangent_series

    The derivative of arctan x is 1 / (1 + x 2); conversely, the integral of 1 / (1 + x 2) is arctan x.

  4. atan2 - Wikipedia

    en.wikipedia.org/wiki/Atan2

    The two figures below show 3D views of respectively atan2(y, x) and arctan(⁠ y / x ⁠) over a region of the plane. Note that for atan2(y, x), rays in the X/Y-plane emanating from the origin have constant values, but for arctan(⁠ y / x ⁠) lines in the X/Y-plane passing through the origin have constant

  5. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    The derivatives in the table above are for when the range of the inverse secant is [,] and when the range of the inverse cosecant is [,]. It is common to additionally define an inverse tangent function with two arguments , arctan ⁡ ( y , x ) {\textstyle \arctan(y,x)} .

  6. Del in cylindrical and spherical coordinates - Wikipedia

    en.wikipedia.org/wiki/Del_in_cylindrical_and...

    The function atan2(y, x) can be used instead of the mathematical function arctan(y/x) owing to its domain and image. The classical arctan function has an image of (−π/2, +π/2), whereas atan2 is defined to have an image of (−π, π].

  7. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    Suppose that a function represents the position of an object at the time. The first derivative of that function is the velocity of an object with respect to time, the second derivative of the function is the acceleration of an object with respect to time, [28] and the third derivative is the jerk. [35]

  8. Taylor series - Wikipedia

    en.wikipedia.org/wiki/Taylor_series

    Second-order Taylor series approximation (in orange) of a function f (x,y) = e x ln(1 + y) around the origin. In order to compute a second-order Taylor series expansion around point (a, b) = (0, 0) of the function (,) = ⁡ (+), one first computes all the necessary partial derivatives:

  9. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    The last expression is the second derivative of position (x) with respect to time. On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the ...