The Power Rule for Derivatives
This animation visualizes the Power Rule by showing f(x)=x³ as a smooth curve that transforms as its exponent slides down to become a coefficient, producing the derivative 3x². The curve morphs to match the new function, linking the algebraic rule to a visual change in shape. A clean summary card displays the general formula d/dx(xⁿ)=n·xⁿ⁻¹. Useful for students beginning differentiation and teachers introducing derivative rules with visual intuition.
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The prompt that made it
Create a 15‑second educational animation showing the Power Rule for derivatives. Begin with a simple function like f(x)=x³ drawn as a smooth curve on a coordinate plane. Animate the exponent ‘3’ sliding down in front of x, transforming the function into 3x². Show the curve morphing to match the new derivative shape. Use bright, clean colors, minimal text, and smooth transitions. End with a quick summary visual: ‘Power Rule: d/dx(xⁿ)=n·xⁿ⁻¹’. Tone: friendly, modern, conceptual.”
Make the next one in this series
- Show the Power Rule applied to negative and fractional exponents like x^-2 and x^(1/2)
- Animate the Product Rule with two curves combining into one derivative
- Visualize why the derivative of a constant is always zero using a flat line
