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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ arcsin(ome^{g}ax + phi)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin(omaxe^{g} + phi)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( arcsin(omaxe^{g} + phi)\right)}{dx}\\=&(\frac{(omae^{g} + omaxe^{g}*0 + 0)}{((1 - (omaxe^{g} + phi)^{2})^{\frac{1}{2}})})\\=&\frac{omae^{g}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{omae^{g}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-o^{2}m^{2}a^{2}*2xe^{{g}*{2}} - o^{2}m^{2}a^{2}x^{2}*2e^{g}e^{g}*0 - 2omaphie^{g} - 2omaphixe^{g}*0 + 0 + 0)}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}})omae^{g} + \frac{omae^{g}*0}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{1}{2}}}\\=&\frac{o^{3}m^{3}a^{3}xe^{{g}*{3}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}} + \frac{o^{2}m^{2}a^{2}phie^{{g}*{2}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{o^{3}m^{3}a^{3}xe^{{g}*{3}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}} + \frac{o^{2}m^{2}a^{2}phie^{{g}*{2}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-o^{2}m^{2}a^{2}*2xe^{{g}*{2}} - o^{2}m^{2}a^{2}x^{2}*2e^{g}e^{g}*0 - 2omaphie^{g} - 2omaphixe^{g}*0 + 0 + 0)}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}})o^{3}m^{3}a^{3}xe^{{g}*{3}} + \frac{o^{3}m^{3}a^{3}e^{{g}*{3}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}} + \frac{o^{3}m^{3}a^{3}x*3e^{{g}*{2}}e^{g}*0}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}} + (\frac{\frac{-3}{2}(-o^{2}m^{2}a^{2}*2xe^{{g}*{2}} - o^{2}m^{2}a^{2}x^{2}*2e^{g}e^{g}*0 - 2omaphie^{g} - 2omaphixe^{g}*0 + 0 + 0)}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}})o^{2}m^{2}a^{2}phie^{{g}*{2}} + \frac{o^{2}m^{2}a^{2}phi*2e^{g}e^{g}*0}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}}\\=&\frac{3o^{5}m^{5}a^{5}x^{2}e^{{g}*{5}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + \frac{6o^{4}m^{4}a^{4}phixe^{{g}*{4}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + \frac{o^{3}m^{3}a^{3}e^{{g}*{3}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}} + \frac{3o^{3}m^{3}a^{3}p^{2}h^{2}i^{2}e^{{g}*{3}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3o^{5}m^{5}a^{5}x^{2}e^{{g}*{5}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + \frac{6o^{4}m^{4}a^{4}phixe^{{g}*{4}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + \frac{o^{3}m^{3}a^{3}e^{{g}*{3}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}} + \frac{3o^{3}m^{3}a^{3}p^{2}h^{2}i^{2}e^{{g}*{3}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-o^{2}m^{2}a^{2}*2xe^{{g}*{2}} - o^{2}m^{2}a^{2}x^{2}*2e^{g}e^{g}*0 - 2omaphie^{g} - 2omaphixe^{g}*0 + 0 + 0)}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{7}{2}}})o^{5}m^{5}a^{5}x^{2}e^{{g}*{5}} + \frac{3o^{5}m^{5}a^{5}*2xe^{{g}*{5}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + \frac{3o^{5}m^{5}a^{5}x^{2}*5e^{{g}*{4}}e^{g}*0}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + 6(\frac{\frac{-5}{2}(-o^{2}m^{2}a^{2}*2xe^{{g}*{2}} - o^{2}m^{2}a^{2}x^{2}*2e^{g}e^{g}*0 - 2omaphie^{g} - 2omaphixe^{g}*0 + 0 + 0)}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{7}{2}}})o^{4}m^{4}a^{4}phixe^{{g}*{4}} + \frac{6o^{4}m^{4}a^{4}phie^{{g}*{4}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + \frac{6o^{4}m^{4}a^{4}phix*4e^{{g}*{3}}e^{g}*0}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + (\frac{\frac{-3}{2}(-o^{2}m^{2}a^{2}*2xe^{{g}*{2}} - o^{2}m^{2}a^{2}x^{2}*2e^{g}e^{g}*0 - 2omaphie^{g} - 2omaphixe^{g}*0 + 0 + 0)}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}})o^{3}m^{3}a^{3}e^{{g}*{3}} + \frac{o^{3}m^{3}a^{3}*3e^{{g}*{2}}e^{g}*0}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{3}{2}}} + 3(\frac{\frac{-5}{2}(-o^{2}m^{2}a^{2}*2xe^{{g}*{2}} - o^{2}m^{2}a^{2}x^{2}*2e^{g}e^{g}*0 - 2omaphie^{g} - 2omaphixe^{g}*0 + 0 + 0)}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{7}{2}}})o^{3}m^{3}a^{3}p^{2}h^{2}i^{2}e^{{g}*{3}} + \frac{3o^{3}m^{3}a^{3}p^{2}h^{2}i^{2}*3e^{{g}*{2}}e^{g}*0}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}}\\=&\frac{15o^{7}m^{7}a^{7}x^{3}e^{{g}*{7}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{7}{2}}} + \frac{45o^{6}m^{6}a^{6}phix^{2}e^{{g}*{6}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{7}{2}}} + \frac{9o^{5}m^{5}a^{5}xe^{{g}*{5}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + \frac{45o^{5}m^{5}a^{5}p^{2}h^{2}i^{2}xe^{{g}*{5}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{7}{2}}} + \frac{9o^{4}m^{4}a^{4}phie^{{g}*{4}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{5}{2}}} + \frac{15o^{4}m^{4}a^{4}p^{3}h^{3}i^{3}e^{{g}*{4}}}{(-o^{2}m^{2}a^{2}x^{2}e^{{g}*{2}} - 2omaphixe^{g} - p^{2}h^{2}i^{2} + 1)^{\frac{7}{2}}}\\ \end{split}\end{equation} \]





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