The most-used differentiation rule.
Drag the point along the curve
y = pow(x, n)at x = 1: slope ≈ 2
Watch the pattern
- d/dx(x) = 1
- d/dx(x²) = 2x
- d/dx(x³) = 3x²
- d/dx(x⁴) = 4x³ — each time: bring the power down, drop it by 1.
Your turn
Differentiate f(x) = 3x⁴ − 2x² + 7.
Watch out
The power rule needs a constant exponent. d/dx(2ˣ) is not x·2ˣ⁻¹ — that's an exponential, handled differently.
Power rule
Try it
d/dx(x⁵)
5x⁴.
Try it
d/dx(√x) = d/dx(x^(1/2))
(1/2)x^(−1/2) = 1/(2√x).