There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 1065.24{(1 - e^{-0.01369x})}^{(\frac{154589}{50000})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 1065.24(-e^{-0.01369x} + 1)^{\frac{154589}{50000}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 1065.24(-e^{-0.01369x} + 1)^{\frac{154589}{50000}}\right)}{dx}\\=&1065.24(3.09178(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}(-e^{-0.01369x}*-0.01369 + 0))\\=&45.087846985368(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 45.087846985368(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}\right)}{dx}\\=&45.087846985368(2.09178(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}(-e^{-0.01369x}*-0.01369 + 0))e^{-0.01369x} + 45.087846985368(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}*-0.01369\\=&1.29115669640296(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} - 0.617252625229688(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 1.29115669640296(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} - 0.617252625229688(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}\right)}{dx}\\=&1.29115669640296(1.09178(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}(-e^{-0.01369x}*-0.01369 + 0))e^{-0.01369x}e^{-0.01369x} + 1.29115669640296(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}*-0.01369e^{-0.01369x} + 1.29115669640296(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x}*-0.01369 - 0.617252625229688(2.09178(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}(-e^{-0.01369x}*-0.01369 + 0))e^{-0.01369x} - 0.617252625229688(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}*-0.01369\\=&0.0192982325040039(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} + 0.00845018843939443(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0.0192982325040039(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} + 0.00845018843939443(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}\right)}{dx}\\=&0.0192982325040039(\frac{0.09178(-e^{-0.01369x}*-0.01369 + 0)}{(-e^{-0.01369x} + 1)^{\frac{45411}{50000}}})e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} + 0.0192982325040039(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}*-0.01369e^{-0.01369x}e^{-0.01369x} + 0.0192982325040039(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}*-0.01369e^{-0.01369x} + 0.0192982325040039(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x}*-0.01369 - 0.0176759351737565(1.09178(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}(-e^{-0.01369x}*-0.01369 + 0))e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}*-0.01369e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x}*-0.01369 - 0.0176759351737565(1.09178(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}(-e^{-0.01369x}*-0.01369 + 0))e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}*-0.01369e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x}*-0.01369 - 0.0176759351737565(1.09178(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}(-e^{-0.01369x}*-0.01369 + 0))e^{-0.01369x}e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}*-0.01369e^{-0.01369x} - 0.0176759351737565(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x}*-0.01369 + 0.00845018843939443(2.09178(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}(-e^{-0.01369x}*-0.01369 + 0))e^{-0.01369x} + 0.00845018843939443(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}*-0.01369\\=&\frac{0.0000242476154574872e^{-0.01369x}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x}}{(-e^{-0.01369x} + 1)^{\frac{45411}{50000}}} - 0.000264192802979813(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} - 0.000264192802979813(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} - 0.000264192802979813(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} - 0.000264192802979813(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} - 0.000264192802979813(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} - 0.000264192802979813(-e^{-0.01369x} + 1)^{\frac{4589}{50000}}e^{-0.01369x}e^{-0.01369x}e^{-0.01369x} + 0.000241983552528726(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} + 0.000241983552528726(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} + 0.000241983552528726(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} + 0.000241983552528726(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} + 0.000241983552528726(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} + 0.000241983552528726(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} + 0.000241983552528726(-e^{-0.01369x} + 1)^{\frac{54589}{50000}}e^{-0.01369x}e^{-0.01369x} - 0.00011568307973531(-e^{-0.01369x} + 1)^{\frac{104589}{50000}}e^{-0.01369x}\\ \end{split}\end{equation} \]

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