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Differentiate the following function w.r.t.x. : xlogx - Mathematics and Statistics

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Question

Differentiate the following function w.r.t.x. : `x/log x`

Sum
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Solution

Let y =`x/log x`

Differentiating w.r.t. x, we get

`dy/dx=d/dx(x/logx)`

= `(logxd/dx(x) - xd/dx(logx))/(logx)^2`

=  `(logx(1) - x(1/x))/(logx)^2`

= `(logx-1)/(logx)^2`

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Rules of Differentiation (Without Proof)
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Chapter 9: Differentiation - Exercise 9.2 [Page 122]

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