Calculus

Product Rule

Derivative of product of functions

  • University
  • about 3 min
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x = 0.50
(x2⋅sin⁡x)′=2x⋅sin⁡x+x2⋅cos⁡x(x^2 \cdot \sin x)' = 2x \cdot \sin x + x^2 \cdot \cos x
x=0.50:  (fg)′=0.699x=0.50: \; (fg)' = 0.699

Product rule: (fg)′ = f′g + fg′. Intuition: the area of rectangle f×g changes when both f and g change simultaneously – hence two terms.