### Higher Order Derivatives Question

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8 months ago by

How to find the fourth derivative for the following function

$f\left(x\right)=4\sqrt[5]{x^3}-\frac{1}{8x^2}-\sqrt{x}$ƒ (x)=45x318x2 x

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8 months ago by

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)=4x35 18 x2x12

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 x25 +14 x312 x12

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 x175 15x6+1516 x72