Find the derivative of the following functions \(\displaystyle{y}={\left({x}^{{{2}}}+{1}\right)}{\ln{{x}}}\)

Javion Kerr 2022-03-22 Answered
Find the derivative of the following functions
y=(x2+1)lnx
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Answers (1)

Esteban Sloan
Answered 2022-03-23 Author has 21 answers
Step 1
Given: y=(x2+1)lnx
we know that
ddx(uv)=vdudx+udvdx...(1)
Step 2
so, by using equation(1)
dydx=ddx[(x2+1)lnx]
=(lnx)ddx(x2+1)+(x2+1)ddx(lnx)
(ddx(xn)=nxn1,ddx(lnx)=1x)
=(lnx)(2x+0)+(x2+1)1x
=2xlnx+x2+1x
hence, derivative of given function is 2xlnx+x2+1x.
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