Higher Order Derivatives Question


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8 months ago by
Justin  

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 

add commentfollow this post modified 8 months ago by Jasmine   • written 8 months ago by Justin  

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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  

 

add comment written 8 months ago by Jasmine  
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