There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (865(1.466 + 0.25 + 0.2 + 0.48) + 350 + 0.012*21000)(1 + (0.01x + 0.05)(0.02(178.7 - x) + 0.5))\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 45.3215366x - 0.253618x^{2} + 6.34045x - 1.26809x + 7.728775x - 0.04325x^{2} + 1.08125x - 0.21625x + 6.18302x - 0.0346x^{2} + 0.865x - 0.173x + 14.839248x - 0.08304x^{2} + 2.076x - 0.4152x + 12.509x - 0.07x^{2} + 1.75x - 0.35x + 9.00648x - 0.0504x^{2} + 1.26x - 0.252x + 3219.343798\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 45.3215366x - 0.253618x^{2} + 6.34045x - 1.26809x + 7.728775x - 0.04325x^{2} + 1.08125x - 0.21625x + 6.18302x - 0.0346x^{2} + 0.865x - 0.173x + 14.839248x - 0.08304x^{2} + 2.076x - 0.4152x + 12.509x - 0.07x^{2} + 1.75x - 0.35x + 9.00648x - 0.0504x^{2} + 1.26x - 0.252x + 3219.343798\right)}{dx}\\=&45.3215366 - 0.253618*2x + 6.34045 - 1.26809 + 7.728775 - 0.04325*2x + 1.08125 - 0.21625 + 6.18302 - 0.0346*2x + 0.865 - 0.173 + 14.839248 - 0.08304*2x + 2.076 - 0.4152 + 12.509 - 0.07*2x + 1.75 - 0.35 + 9.00648 - 0.0504*2x + 1.26 - 0.252 + 0\\=& - 0.507236x - 0.0865x - 0.0692x - 0.16608x - 0.14x - 0.1008x + 106.2862196\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!