Differential Calculus
Derivatives and differentiation expressions.
Differential calculus is a subfield of calculus that studies the rates at which quantities change.
| Expression | 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) |
