What is the second derivative of # (x^2 + 1/x)^5#?

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What is the second derivative of # (x^2 + 1/x)^5#?

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Answer 1 · 2018-06-02T17:16:28

#f''(x)=20(x^2+1/x)^3(2x-1/x^2)^2+5(x^2+1/x)^4(2+2+2/x^3)#

Explanation:

We have
#f(x)=(x^2+1/x)^5#
after the chain and the power rule we get
#f'(x)=5(x^2+1/x)^4(2x-1/x^2)#
#f''(x)=20(x^2+1/x)^3(2x-1/x^2)^2+5(x^2+1/x)^4(2+2/x^3)#

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What is the second derivative of # (x^2 + 1/x)^5#?

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