Leibniz integral rule

Summary

Leibniz integral rule is a theorem^[1]. It ranks in the top 2% of theorem entities by monthly Wikipedia readership (707 views/month).^[2]

Key Facts

• Leibniz integral rule's instance of is recorded as theorem^[3].
• Leibniz integral rule's instance of is recorded as differentiation rule^[4].
• Gottfried Wilhelm Leibniz is named after Leibniz integral rule^[5].
• Leibniz integral rule's has use is recorded as integral^[6].
• Leibniz integral rule's has use is recorded as derivative^[7].
• Leibniz integral rule's has use is recorded as differentiation of integrals^[8].
• Leibniz integral rule's Freebase ID is recorded as /m/07mzf7^[9].
• Leibniz integral rule's uses is recorded as parametric integral^[10].
• Leibniz integral rule's defining formula is recorded as \frac{\mathrm{d}}{\mathrm{d}x} \int_{\alpha(x)}^{\beta(x)} f(x, y) \, \mathrm{d}y = f(x, \beta(x)) \beta'(x) - f(x, \alpha(x)) \alpha'(x) + \int_{\alpha(x)}^{\beta(x)} \frac{\partial f(x, y)}{\partial x} \, \mathrm{d}y^[11].
• Leibniz integral rule's studied by is recorded as calculus^[12].
• Leibniz integral rule's MathWorld ID is recorded as LeibnizIntegralRule^[13].
• Leibniz integral rule's maintained by WikiProject is recorded as WikiProject Mathematics^[14].
• Leibniz integral rule's Microsoft Academic ID is recorded as 183218574^[15].
• Leibniz integral rule's Microsoft Academic ID is recorded as 156532913^[16].
• Leibniz integral rule's Brilliant Wiki ID is recorded as differentiate-through-the-integral^[17].
• Leibniz integral rule's in defining formula is recorded as f^[18].
• Leibniz integral rule's in defining formula is recorded as \frac{\mathrm{d}}{\mathrm{d}x}^[19].
• Leibniz integral rule's in defining formula is recorded as \int_a^b f(x) \, \mathrm{d}x^[20].
• Leibniz integral rule's in defining formula is recorded as '^[21].
• Leibniz integral rule's in defining formula is recorded as \frac{\partial}{\partial x}^[22].
• Leibniz integral rule's Digital Library of Mathematical Functions ID is recorded as 1.5.E22^[23].

Why It Matters

Leibniz integral rule ranks in the top 2% of theorem entities by monthly Wikipedia readership (707 views/month).^[2] It has Wikipedia articles in 14 language editions, a strong signal of global cultural recognition.^[24] It is known by 6 alternative names across languages and contexts.^[25]