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Find dydxif y = x log x (x2 + 1) - Mathematics and Statistics

Sum

Find `dy/dx`if y = x log x (x2 + 1)

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Solution

y = x log x (x2 + 1)
Differentiating w.r.t. x, we get

`dy/dx = d/dx(x)(logx)(x^2 + 1)`

= `(x)(logx)d/dx(x^2 + 1) - (x^2 + 1)d/dx((x)(logx))`

= `(xlogx)(2x + 0) + (x^2 + 1)[xd/dx(logx) + (logx)d/dx(x)]`

=`2x^2logx + (x^2 + 1)[x xx 1/x + (logx)(1)]`

= 2x2 log x + (x2 + 1) (1 + log x)
= 2x2 log x + (x2 + 1) + (x2 + 1) log x

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 9 Differentiation
Miscellaneous Exercise 9 | Q II. (10) | Page 123
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