Differentiation

• f(x)=k ln⁡(ax) ⟶ f′(x)=k/x
• f(x) = k logb(ax) → f'(x) = k/x logb(e)
• change of base: loga(x) = loga(b) ・logb(x)
• sin(kx) → kcos(kx)
• cos(kx) → -ksin(kx)
• tan(kx) → ksec^2 (kx)
• cot(kx) → - kcosec^2 (kx)
• sec(kx) → ksec(kx)tan(kx)
• cosec(kx) → -kcosec(kx)cot(kx)
• prove gradient function: use first principles