12. Find the differential coefficient of (x2+7) (x2+10)

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Eawer asked Feb 19, 2023

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38 votes

12. Find the differential coefficient of (x2+7) (x2+10)

Mathematics
high-school

Eawer asked Feb 19, 2023

by Eawer

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1 Answer

17 votes

Answer:

$We \: need \: to \: find \\ the \: differential \\ coefficient \: of \: the \\ function  \: x2logxsinx  \\ with \: respect \: to \:  x. \\Let  \: y=x \: 2logxsinx \\ We \: need \\ to \: find \:  dxdy. \\Consider  \\ y=x \: 2logxsinx \\ dxdy=dxd(x2)logxsinx+x2dxd(logxsinx) \\  =2x(logxsinx)+x2[sinxdxd(logx)+logxdxd(sinx)] \\ =2x(logxsinx)+x2[xsinx+logxcosx] \\ dxdy=2x(logxsinx)+xsinx+x2logxcosx$