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Given the following, I am asked to calculate the elasticity of wages with respect to age:

$$𝑙𝑛(𝑤_𝑖)=𝛽_1+𝛽_2𝑎𝑔𝑒_i+𝛽_3𝑎𝑔𝑒^2_𝑖+𝛽_4𝑌_𝑖+𝛽_5𝑇_𝑖+𝛽_6𝑀𝑎𝑟_𝑖+𝜖_𝑖$$

How does one calculate a full elasticity between a log variable and and non-log variable? Is the following attempt correct?

$$\frac{\partial ln(w)}{{\frac{\partial age}{age}}}=\frac{\partial ln(w)}{\partial age}age=(\beta_2+2\beta_3age)(age)$$

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