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 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {x}^{5} - 4{x}^{3} + \frac{3}{x}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{5} - 4x^{3} + \frac{3}{x}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x^{5} - 4x^{3} + \frac{3}{x}\right)}{dx}\\=&5x^{4} - 4*3x^{2} + \frac{3*-1}{x^{2}}\\=&5x^{4} - 12x^{2} - \frac{3}{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 5x^{4} - 12x^{2} - \frac{3}{x^{2}}\right)}{dx}\\=&5*4x^{3} - 12*2x - \frac{3*-2}{x^{3}}\\=&20x^{3} - 24x + \frac{6}{x^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 20x^{3} - 24x + \frac{6}{x^{3}}\right)}{dx}\\=&20*3x^{2} - 24 + \frac{6*-3}{x^{4}}\\=&60x^{2} - \frac{18}{x^{4}} - 24\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 60x^{2} - \frac{18}{x^{4}} - 24\right)}{dx}\\=&60*2x - \frac{18*-4}{x^{5}} + 0\\=&120x + \frac{72}{x^{5}}\\ \end{split}\end{equation} \]





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