Differentiation equations

• y = sin kx, dy⁄dx = k cos kx
• y = cos kx, dy⁄dx = -k sin kx
• y = e^kx, dy⁄dx = ke^kx
• y = ln x, dy⁄dx = 1/x
• y = a^kx, dy⁄dx = a^kxk ln(a)
• y = tan kx, dy⁄dx = k sec² kx
• y = cosec ks, dy⁄dx = -k cosec kx cot kx
• y = sec kx, dy⁄dx = k sec kx tan kx
• y = cot kx, dy⁄dx = -k cosec² kx

Differentiation rules

• Chain rule
  dy⁄dx = dy⁄du x du⁄dx
• Product rule
  y = uv, dy⁄dx = u(dv⁄dx) + v(du⁄dx)
• Quotient rule
  y = u ⁄ v, dy⁄dx = (v(du⁄dx) - u(dv⁄dx) ⁄ v²