Power Rule
\(\frac{d}{dx}[x^3] = 3x^2\)
微分計算機
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結果
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理論と公式
The derivative measures the rate of change of a function at any given point. It represents the slope of the tangent line to the function at that point.
Common derivative rules:
- Power Rule: \(\frac{d}{dx}[x^n] = nx^{n-1}\)
- Constant Rule: \(\frac{d}{dx}[c] = 0\)
- Sum Rule: \(\frac{d}{dx}[f + g] = f' + g'\)
- Product Rule: \(\frac{d}{dx}[fg] = f'g + fg'\)
- Trigonometric: \(\frac{d}{dx}[\sin(x)] = \cos(x)\), \(\frac{d}{dx}[\cos(x)] = -\sin(x)\)
- Exponential: \(\frac{d}{dx}[e^x] = e^x\)
解説付き例題
Trigonometric
\(\frac{d}{dx}[\sin(x)] = \cos(x)\)
Exponential
\(\frac{d}{dx}[e^x] = e^x\)