# Differential Calculus

## Derivatives and differentiation

ExpressionDerivatives
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)

## Related Topics

• Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more

## Search the Engineering ToolBox

- "the most efficient way to navigate!"

## Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!

close