There are 1 questions in this calculation: for each question, the 1 derivative of d is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{csqrt(\frac{1}{(2lln(\frac{b}{a})(\frac{1}{d} + \frac{4ln(\frac{(esqrt(({b}^{2} - {a}^{2}) + {(l + d)}^{2}))}{(2d)})}{(pia)}))})}{(api)}\ with\ respect\ to\ d:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{csqrt(\frac{1}{(\frac{2lln(\frac{b}{a})}{d} + \frac{8lln(\frac{b}{a})ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api})})}{api}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{csqrt(\frac{1}{(\frac{2lln(\frac{b}{a})}{d} + \frac{8lln(\frac{b}{a})ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api})})}{api}\right)}{dd}\\=&\frac{c(\frac{-(\frac{2l*-ln(\frac{b}{a})}{d^{2}} + \frac{2l*0}{d(\frac{b}{a})} + \frac{8l*0ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api(\frac{b}{a})} + \frac{8lln(\frac{b}{a})(\frac{\frac{1}{2}*-esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d^{2}} + \frac{\frac{1}{2}*0sqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d} + \frac{\frac{1}{2}e(0 + 0 + 2l + 0 + 2d)*\frac{1}{2}}{d(b^{2} - a^{2} + 2ld + l^{2} + d^{2})^{\frac{1}{2}}})}{api(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})})}{(\frac{2lln(\frac{b}{a})}{d} + \frac{8lln(\frac{b}{a})ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api})^{2}})*\frac{1}{2}}{api(\frac{1}{(\frac{2lln(\frac{b}{a})}{d} + \frac{8lln(\frac{b}{a})ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api})})^{\frac{1}{2}}}\\=&\frac{clln(\frac{b}{a})}{(\frac{2lln(\frac{b}{a})}{d} + \frac{8lln(\frac{b}{a})ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api})^{\frac{3}{2}}apid^{2}} + \frac{4clln(\frac{b}{a})}{(\frac{2lln(\frac{b}{a})}{d} + \frac{8lln(\frac{b}{a})ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api})^{\frac{3}{2}}a^{2}p^{2}i^{2}d} - \frac{4cl^{2}ln(\frac{b}{a})}{(\frac{2lln(\frac{b}{a})}{d} + \frac{8lln(\frac{b}{a})ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api})^{\frac{3}{2}}(b^{2} - a^{2} + 2ld + l^{2} + d^{2})^{\frac{1}{2}}a^{2}p^{2}i^{2}sqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})} - \frac{4cldln(\frac{b}{a})}{(\frac{2lln(\frac{b}{a})}{d} + \frac{8lln(\frac{b}{a})ln(\frac{\frac{1}{2}esqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}{d})}{api})^{\frac{3}{2}}(b^{2} - a^{2} + 2ld + l^{2} + d^{2})^{\frac{1}{2}}a^{2}p^{2}i^{2}sqrt(b^{2} - a^{2} + 2ld + l^{2} + d^{2})}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!