Mathematics
语言:中文
Language:English

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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (1 - ln(x)){\frac{1}{x}}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{ln(x)}{x^{2}} + \frac{1}{x^{2}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( - \frac{ln(x)}{x^{2}} + \frac{1}{x^{2}}\right)}{dx}\\=& - \frac{-2ln(x)}{x^{3}} - \frac{1}{x^{2}(x)} + \frac{-2}{x^{3}}\\=&\frac{2ln(x)}{x^{3}} - \frac{3}{x^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2ln(x)}{x^{3}} - \frac{3}{x^{3}}\right)}{dx}\\=&\frac{2*-3ln(x)}{x^{4}} + \frac{2}{x^{3}(x)} - \frac{3*-3}{x^{4}}\\=& - \frac{6ln(x)}{x^{4}} + \frac{11}{x^{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{6ln(x)}{x^{4}} + \frac{11}{x^{4}}\right)}{dx}\\=& - \frac{6*-4ln(x)}{x^{5}} - \frac{6}{x^{4}(x)} + \frac{11*-4}{x^{5}}\\=&\frac{24ln(x)}{x^{5}} - \frac{50}{x^{5}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{24ln(x)}{x^{5}} - \frac{50}{x^{5}}\right)}{dx}\\=&\frac{24*-5ln(x)}{x^{6}} + \frac{24}{x^{5}(x)} - \frac{50*-5}{x^{6}}\\=& - \frac{120ln(x)}{x^{6}} + \frac{274}{x^{6}}\\ \end{split}\end{equation} \]





Your problem has not been solved here? Please take a look at the  hot problems !


Return