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if y=x^x find  δy/δx - CBSE (Science) Class 12 - Mathematics

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Question

if `y=x^x` find `(dy)/(dx)`

Solution

`y=x^x`

Taking logarithms of both sides

`logy=logx^x`

`logy=xlogx`

Differentiating both sides with respect to 'x', we get

`(1/y) dy/dx=x(1/x)+logx(1)`

`dy/dx=y(1+logx)`

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

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APPEARS IN

 2015-2016 (March) (with solutions)
Question 4.2.1 | 2.00 marks
Solution if y=x^x find  δy/δx Concept: Exponential and Logarithmic Functions.
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