There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-(cos(x) + 5x + 1)sin(x)*3(cos(x) + 5x + 1)}{3} + \frac{5(cos(x) + 5x + 1)(cos(x) + 5x + 1)}{3}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -sin(x)cos^{2}(x) - 10xsin(x)cos(x) - 2sin(x)cos(x) - 25x^{2}sin(x) - 10xsin(x) - sin(x) + \frac{5}{3}cos^{2}(x) + \frac{50}{3}xcos(x) + \frac{10}{3}cos(x) + \frac{125}{3}x^{2} + \frac{50}{3}x + \frac{5}{3}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( -sin(x)cos^{2}(x) - 10xsin(x)cos(x) - 2sin(x)cos(x) - 25x^{2}sin(x) - 10xsin(x) - sin(x) + \frac{5}{3}cos^{2}(x) + \frac{50}{3}xcos(x) + \frac{10}{3}cos(x) + \frac{125}{3}x^{2} + \frac{50}{3}x + \frac{5}{3}\right)}{dx}\\=&-cos(x)cos^{2}(x) - sin(x)*-2cos(x)sin(x) - 10sin(x)cos(x) - 10xcos(x)cos(x) - 10xsin(x)*-sin(x) - 2cos(x)cos(x) - 2sin(x)*-sin(x) - 25*2xsin(x) - 25x^{2}cos(x) - 10sin(x) - 10xcos(x) - cos(x) + \frac{5}{3}*-2cos(x)sin(x) + \frac{50}{3}cos(x) + \frac{50}{3}x*-sin(x) + \frac{10}{3}*-sin(x) + \frac{125}{3}*2x + \frac{50}{3} + 0\\=&-cos^{3}(x) + 2sin^{2}(x)cos(x) - \frac{40sin(x)cos(x)}{3} - 10xcos^{2}(x) + 10xsin^{2}(x) - 2cos^{2}(x) + 2sin^{2}(x) - \frac{200xsin(x)}{3} - 25x^{2}cos(x) - \frac{40sin(x)}{3} - 10xcos(x) + \frac{47cos(x)}{3} + \frac{250x}{3} + \frac{50}{3}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!