anonymous
  • anonymous
What is the second derivative of cube root of (x^2-1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Owlcoffee
  • Owlcoffee
\[f:f(x)=\sqrt[3]{(x^2-1}\] You can make use of the exponential property \(\sqrt[n]{A}=A ^{\frac{ 1 }{ n }}\) which will simplify the derivation of this function thereby performin the transformation \(f:f(x)\rightarrow f':f'(x)\) : \[f:f(x)=(x^2-1)^{\frac{ 1 }{ 3 }}\] \[f':f'(x)=\frac{ 1 }{ 3 }(x^2-1)^{(\frac{ 1 }{ 3 }-1)}(2x)\] Remember that \(f(x)=\sqrt[3]{x^2-1}\) is a composite function, because we don't have a positive "x" alone inside the root, which means we have to use the derivation rule: \(H(x)=g(f(x)) \iff H'(x)=g'(f(x)).f'(x)\).
Owlcoffee
  • Owlcoffee
after you operate that, you derivate again to obtain the second derivative.
anonymous
  • anonymous
Refer to the attachment.
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