There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{((2(arctan(\frac{4.85}{(10 + x)}) + arctan(\frac{10}{sqrt({4.85}^{2} + 100 - {(10 + x)}^{2})})) - 90)*3.1415926)}{18} + 2sqrt({4.85}^{2} + 100 - {(10 + x)}^{2}) - 25.4\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 0.349065844444444arctan(\frac{4.85}{(x + 10)}) + 0.349065844444444arctan(\frac{10}{sqrt(-x + 94.85)}) + 2sqrt(-x + 94.85) - 41.107963\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 0.349065844444444arctan(\frac{4.85}{(x + 10)}) + 0.349065844444444arctan(\frac{10}{sqrt(-x + 94.85)}) + 2sqrt(-x + 94.85) - 41.107963\right)}{dx}\\=&0.349065844444444(\frac{(4.85(\frac{-(1 + 0)}{(x + 10)^{2}}))}{(1 + (\frac{4.85}{(x + 10)})^{2})}) + 0.349065844444444(\frac{(\frac{10*-(-1 + 0)*0.5}{(-x + 94.85)(-x + 94.85)^{\frac{1}{2}}})}{(1 + (\frac{10}{sqrt(-x + 94.85)})^{2})}) + \frac{2(-1 + 0)*0.5}{(-x + 94.85)^{\frac{1}{2}}} + 0\\=&\frac{1.74532922222222}{(-x + 94.85)(-x + 94.85)^{\frac{1}{2}}(\frac{100}{sqrt(-x + 94.85)^{2}} + 1)} - \frac{1.69296934555556}{(x + 10)(x + 10)(\frac{23.5225}{(x + 10)(x + 10)} + 1)} - \frac{1}{(-x + 94.85)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!