Differential Calculus

Derivatives and differentiation expressions. A subfield of calculus that studies the rates at which quantities change.

Differential Calculus

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

Common Derivatives

This table provides derivatives for common mathematical expressions and functions.

ExpressionDerivative
y = xⁿdy/dx = n xⁿ⁻¹
y = a xⁿdy/dx = a n xⁿ⁻¹
f(x) = a xⁿf'(x) = a n xⁿ⁻¹
y = eˣdy/dx = eˣ
y = eᵃˣdy/dx = a eᵃˣ
y = aˣdy/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)
y = cos⁻¹(x / a)dy/dx = -1 / √(a² - x²)
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))
y = cosec⁻¹(x / a)dy/dx = -a / (x √(x² - a²))
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