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What are the rules of differentiation?
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Rules for differentiation
- General rule for differentiation:
$\frac{d}{d x}\left[x^{n}\right]=n x^{n-1}, \text { where } n \in \mathbb{R} \text { and } n \neq 0$
- The derivative of a constant is equal to zero.
$\frac{d}{d x}[k]=0$
- The derivative of a constant multiplied by a function is equal to the constant multiplied by the derivative of the function.
$\frac{d}{d x}[k \cdot f(x)]=k \frac{d}{d x}[f(x)]$
- The derivative of a sum is equal to the sum of the derivatives.
$\frac{d}{d x}[f(x)+g(x)]=\frac{d}{d x}[f(x)]+\frac{d}{d x}[g(x)]$
- The derivative of a difference is equal to the difference of the derivatives.
$\frac{d}{d x}[f(x)-g(x)]=\frac{d}{d x}[f(x)]-\frac{d}{d x}[g(x)]$
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