Derivative Rules

d/dx (c) where c is any constant

d/dx (c) = 0

d/dx (xᶜ) where c is any constant

d/dx (xᶜ) = cxᶜ⁻¹

d/dx (x) where x is a variable

d/dx (x) = 1

d/dx (bˣ) where b is any positive constant

d/dx (bˣ) = bˣ ⋅ ln(b)

d/dx (logₙ(x)) where n is any positive constant

d/dx (logₙ(x)) = 1/(x ⋅ ln(n))

d/dx (f(x) ⋅ g(x))

d/dx (f(x) ⋅ g(x)) = (f(x) ⋅ g’(x)) + (f’(x) ⋅ g(x))

d/dx (f(x)/g(x))

d/dx (f(x)/g(x)) = (( low ⋅ D_high ) - ( high D_low )) / ( low ⋅ low )

Chain Rule

used for composite functions
ex: f(g(x))

basically do the normal rules as they apply, then multiply by u’ at the end

d/dx (uⁿ) = nuⁿ⁻¹ ⋅ u’
where u is something you can derive on its own

ex: d/dx (4x³ + 5x² + 9)⁷ = 7(4x³ + 5x² + 9)⁶ ⋅ (12x² + 10x + 9)