Math 22 Differentials and Marginal Analysis

Differentials

 Let $y=f(x)$ represent a differentiable function. The differential of $x$ (denoted by $dx$)
 is any nonzero real number. The differential of $y$ (denoted by ) is $dy=f'(x)dx$.

Example: Consider the function $f(x)=3x^{3}$. Find $dy$ when $x=1$ and $dx=0.01$

Solution:
Notice: $f(x)=3x^{3}$, so $dy=f'(x)dx=9x^{2}dx=9(1)^{2}.(0.01)=0.09$

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