There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(2{a}^{2}{x}^{3} + (-{a}^{2}H + 2aH - H){x}^{2} + (a{H}^{2} + {H}^{2})x)}{({x}^{2} - {a}^{2}{H}^{2})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2a^{2}x^{3}}{(x^{2} - a^{2}H^{2})} - \frac{a^{2}Hx^{2}}{(x^{2} - a^{2}H^{2})} + \frac{2aHx^{2}}{(x^{2} - a^{2}H^{2})} - \frac{Hx^{2}}{(x^{2} - a^{2}H^{2})} + \frac{aH^{2}x}{(x^{2} - a^{2}H^{2})} + \frac{H^{2}x}{(x^{2} - a^{2}H^{2})}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{2a^{2}x^{3}}{(x^{2} - a^{2}H^{2})} - \frac{a^{2}Hx^{2}}{(x^{2} - a^{2}H^{2})} + \frac{2aHx^{2}}{(x^{2} - a^{2}H^{2})} - \frac{Hx^{2}}{(x^{2} - a^{2}H^{2})} + \frac{aH^{2}x}{(x^{2} - a^{2}H^{2})} + \frac{H^{2}x}{(x^{2} - a^{2}H^{2})}\right)}{dx}\\=&2(\frac{-(2x + 0)}{(x^{2} - a^{2}H^{2})^{2}})a^{2}x^{3} + \frac{2a^{2}*3x^{2}}{(x^{2} - a^{2}H^{2})} - (\frac{-(2x + 0)}{(x^{2} - a^{2}H^{2})^{2}})a^{2}Hx^{2} - \frac{a^{2}H*2x}{(x^{2} - a^{2}H^{2})} + 2(\frac{-(2x + 0)}{(x^{2} - a^{2}H^{2})^{2}})aHx^{2} + \frac{2aH*2x}{(x^{2} - a^{2}H^{2})} - (\frac{-(2x + 0)}{(x^{2} - a^{2}H^{2})^{2}})Hx^{2} - \frac{H*2x}{(x^{2} - a^{2}H^{2})} + (\frac{-(2x + 0)}{(x^{2} - a^{2}H^{2})^{2}})aH^{2}x + \frac{aH^{2}}{(x^{2} - a^{2}H^{2})} + (\frac{-(2x + 0)}{(x^{2} - a^{2}H^{2})^{2}})H^{2}x + \frac{H^{2}}{(x^{2} - a^{2}H^{2})}\\=&\frac{-4a^{2}x^{4}}{(x^{2} - a^{2}H^{2})^{2}} + \frac{6a^{2}x^{2}}{(x^{2} - a^{2}H^{2})} + \frac{2a^{2}Hx^{3}}{(x^{2} - a^{2}H^{2})^{2}} - \frac{2a^{2}Hx}{(x^{2} - a^{2}H^{2})} - \frac{4aHx^{3}}{(x^{2} - a^{2}H^{2})^{2}} + \frac{4aHx}{(x^{2} - a^{2}H^{2})} + \frac{2Hx^{3}}{(x^{2} - a^{2}H^{2})^{2}} - \frac{2Hx}{(x^{2} - a^{2}H^{2})} - \frac{2aH^{2}x^{2}}{(x^{2} - a^{2}H^{2})^{2}} + \frac{aH^{2}}{(x^{2} - a^{2}H^{2})} - \frac{2H^{2}x^{2}}{(x^{2} - a^{2}H^{2})^{2}} + \frac{H^{2}}{(x^{2} - a^{2}H^{2})}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!