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# Differential Calculus

## Derivatives and differentiation expressions.

Differential calculus is a subfield of calculus that studies the rates at which quantities change.

Differential Calculus - Derivatives
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)

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## Citation

• The Engineering ToolBox (2011). Differential Calculus. [online] Available at: https://www.engineeringtoolbox.com/derivatives-differential-calculus-d_1766.html [Accessed Day Month Year].

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12.8.9