Most derivatives can be computed with four rules. Memorise these and you can differentiate almost any reasonable function.
The four rules
- Power: d/dx(xⁿ) = n·xⁿ⁻¹
- Sum: (f + g)' = f' + g'
- Product: (f·g)' = f'·g + f·g'
- Chain: (f(g(x)))' = f'(g(x)) · g'(x)
Try it
d/dx(3x⁴)
Power rule: 3 · 4x³ = 12x³.
Try it
d/dx(sin(x²))
Chain rule: cos(x²) · 2x = 2x·cos(x²).