Calculating Derivatives #
The derivative measures the rate of change of a function. Geometrically, it’s the slope of the tangent line.
Fundamental Derivatives #
| \(f(x)\) | \(f’(x)\) |
|---|---|
| \(c\) | \(0\) |
| \(x^n\) | \(n \cdot x^{n-1}\) |
| \(e^x\) | \(e^x\) |
| \(\ln x\) | \(1/x\) |
| \(\sin x\) | \(\cos x\) |
| \(\cos x\) | \(-\sin x\) |
Rules #
- Constant multiple: \([c \cdot f]’ = c \cdot f’\)
- Sum: \([f \pm g]’ = f’ \pm g’\)
Example: \(f(x) = 3x^4 + 2x^2 - 5x + 7 \implies f’(x) = 12x^3 + 4x - 5\)
Reply by Email📝 Mnemonic: “Bring down the exponent, reduce it by one.”