### Higher Order Derivatives Question

### 1 Answer

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Not much to this problem other than to take four derivatives so each step will show each successive derivatives until we get to the fourth. After a quick rewrite of the function to help with the differentiation the first derivative is,

$f\left(x\right)=4x^{\frac{3}{5}}-\frac{1}{8}x^{-2}-x^{\frac{1}{2}}$`ƒ` (`x`)=4`x`^{35 }−18 `x`^{−2}−`x`^{12 }

1st derivative

$f'\left(x\right)=\frac{12}{5}x^{-\frac{2}{5}}+\frac{1}{4}x^{-3}-\frac{1}{2}x^{-\frac{1}{2}}$`ƒ` '(`x`)=125 `x`^{−25 }+14 `x`^{−3}−12 `x`^{−12 }

and so on until we get the fourth derivative

$f^{\left(4\right)}\left(x\right)=-\frac{2016}{625}x^{-\frac{17}{5}}-15x^{-6}+\frac{15}{16}x^{-\frac{7}{2}}$`ƒ` ^{(4)}(`x`)=−2016625 `x`^{−175 }−15`x`^{−6}+1516 `x`^{−72 }

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written
8 months ago by
Jasmine

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