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Derivatives and differentiation expressions.
Differential calculus is a subfield of calculus that studies the rates at which quantities change.
Differential Calculus - Derivatives
|y = xn ||dy/dx = n xn-1 |
|y = a xn ||dy/dx = a n xn-1 |
|f(x) = a xn ||f'(x) = a n xn-1 |
|y = ex ||dy/dx = ex |
|y = ea x ||dy/dx = a ea x |
|y = ax ||dy/dx = ax ln(a) |
|y = ln(x) ||dy/dx = 1 / x |
|y = sin(Θ) ||dy/dΘ = cos(Θ) |
|y = cos(Θ) ||dy/dΘ = - sin(Θ) |
|y = tan(Θ) ||dy/dΘ = sec2(Θ) |
|y = cot(Θ) ||dy/dΘ = cosec2(Θ) |
|y = sec(Θ) ||dy/dΘ = tan(Θ) sec(Θ) |
= sin(Θ) / cos2(Θ)
|y = cosec(Θ) ||dy/dΘ = - cot(Θ) cosec(Θ) |
= - cos(Θ) / sin2(Θ)
|y = sin-1(x / a) ||dy/dx = 1 / (a2 - x2)1/2 |
|y = cos-1(x / a) ||dy/dx = - 1 / (a2 - x2)1/2 |
|y = tan-1(x / a) ||dy/dx = a / (a2 + x2) |
|y = cot-1(x / a) ||dy/dx = - a / (a2 + x2) |
|y = sec-1(x / a) ||dy/dx = a / (x (x2 - a2)1/2) |
|y = cosec-1(x / a) ||dy/dx = - a / (x (x2 - a2)1/2) |
- Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.
- Complex numbers are used in alternating current theory and mechanical vector analysis.
- The mathematical π constants.
- The mathematical e constants.
- The laws of fractional and integer exponents.
- The product of all positive integers.
- Law of fractions
- Convert between Cartesian and Polar coordinates.
- Equations for differentials and integrals.
- Function as an infinite sum of terms.
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