Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ a - b{10}^{(\frac{x}{10})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = a - b{10}^{(\frac{1}{10}x)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( a - b{10}^{(\frac{1}{10}x)}\right)}{dx}\\=&0 - b({10}^{(\frac{1}{10}x)}((\frac{1}{10})ln(10) + \frac{(\frac{1}{10}x)(0)}{(10)}))\\=& - \frac{b{10}^{(\frac{1}{10}x)}ln(10)}{10}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{b{10}^{(\frac{1}{10}x)}ln(10)}{10}\right)}{dx}\\=& - \frac{b({10}^{(\frac{1}{10}x)}((\frac{1}{10})ln(10) + \frac{(\frac{1}{10}x)(0)}{(10)}))ln(10)}{10} - \frac{b{10}^{(\frac{1}{10}x)}*0}{10(10)}\\=& - \frac{b{10}^{(\frac{1}{10}x)}ln^{2}(10)}{100}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{b{10}^{(\frac{1}{10}x)}ln^{2}(10)}{100}\right)}{dx}\\=& - \frac{b({10}^{(\frac{1}{10}x)}((\frac{1}{10})ln(10) + \frac{(\frac{1}{10}x)(0)}{(10)}))ln^{2}(10)}{100} - \frac{b{10}^{(\frac{1}{10}x)}*2ln(10)*0}{100(10)}\\=& - \frac{b{10}^{(\frac{1}{10}x)}ln^{3}(10)}{1000}\\ \end{split}\end{equation} \]





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