Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 1 derivative of y is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(y + {(\frac{y}{(4(fR + h))} - (R + h))}^{2}) - R\ with\ respect\ to\ y:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(y + \frac{y^{2}}{(4fR + 4h)^{2}} - \frac{2Ry}{(4fR + 4h)} - \frac{2hy}{(4fR + 4h)} + 2Rh + R^{2} + h^{2}) - R\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( sqrt(y + \frac{y^{2}}{(4fR + 4h)^{2}} - \frac{2Ry}{(4fR + 4h)} - \frac{2hy}{(4fR + 4h)} + 2Rh + R^{2} + h^{2}) - R\right)}{dy}\\=&\frac{(1 + (\frac{-2(0 + 0)}{(4fR + 4h)^{3}})y^{2} + \frac{2y}{(4fR + 4h)^{2}} - 2(\frac{-(0 + 0)}{(4fR + 4h)^{2}})Ry - \frac{2R}{(4fR + 4h)} - 2(\frac{-(0 + 0)}{(4fR + 4h)^{2}})hy - \frac{2h}{(4fR + 4h)} + 0 + 0 + 0)*\frac{1}{2}}{(y + \frac{y^{2}}{(4fR + 4h)^{2}} - \frac{2Ry}{(4fR + 4h)} - \frac{2hy}{(4fR + 4h)} + 2Rh + R^{2} + h^{2})^{\frac{1}{2}}} + 0\\=& - \frac{R}{(4fR + 4h)(y + \frac{y^{2}}{(4fR + 4h)^{2}} - \frac{2Ry}{(4fR + 4h)} - \frac{2hy}{(4fR + 4h)} + 2Rh + R^{2} + h^{2})^{\frac{1}{2}}} + \frac{y}{(4fR + 4h)^{2}(y + \frac{y^{2}}{(4fR + 4h)^{2}} - \frac{2Ry}{(4fR + 4h)} - \frac{2hy}{(4fR + 4h)} + 2Rh + R^{2} + h^{2})^{\frac{1}{2}}} - \frac{h}{(4fR + 4h)(y + \frac{y^{2}}{(4fR + 4h)^{2}} - \frac{2Ry}{(4fR + 4h)} - \frac{2hy}{(4fR + 4h)} + 2Rh + R^{2} + h^{2})^{\frac{1}{2}}} + \frac{1}{2(y + \frac{y^{2}}{(4fR + 4h)^{2}} - \frac{2Ry}{(4fR + 4h)} - \frac{2hy}{(4fR + 4h)} + 2Rh + R^{2} + h^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]





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