Function Differentiation Task

A Function Differentiation Task is a mathematical task that requires the derivative of a function.

• AKA: Derivative Function Identification.
• Context:
  • Input: Differentiable Function.
  • It can range from being a Manual Function Differentiation Task to being an Automated Function Differentiation Task.
  • It can be solved by a Function Differentiation System.
  • …
• See: Gradient Function.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/derivative Retrieved:2015-1-11.
  • The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function or dependent variable) which is determined by another quantity (the independent variable). It is a fundamental tool of calculus. …

    … The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.

2009

• http://www.euclideanspace.com/maths/differential/vectorcalculus/index.htm
  • Differentiation with respect to a scalar is defined as follows, if:
    • f(x) = [a, b, c, Daniel S. Weld.
  • then:
    • d f(x) / dx = [d(a /dx), d(b/dx), d(c/dx), d(e/dx)]
  • In other words to differentiate with respect to a scalar, we just differentiate the elements individually. So to give a more specific example if:
    • f(x) = [xn, sin(x), tan(x), ex]
  • then:
    • d f(x) / dx = [n*xn-1, cos(x), sec2(x), ex]
  • So this is quite simple, provided that we can differentiate the elements of a vector, we can differentiate the whole quaternion.

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