Question

13. If y=x*then the value of dy/dx is

JEE/Engineering Exams

Maths

Solution

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( y=x^{x^{x}} ) ( log y=x^{x} log x ) ( Rightarrow quad z=x^{x} ) ( Rightarrow quad log _{j}=x log x ) ( Rightarrow frac{1}{3} frac{d g}{d x}=(1+log x) ) ( Rightarrow quad frac{d_{3}}{d x}=x^{x}(1+log x) ) from (1) ( log y=x^{2} log x ) ( Rightarrow frac{1}{y} frac{d y}{d x}=x^{x}(17 lg x) log x+frac{x^{x}}{x} ) ( Rightarrow frac{d y}{d x}=x^{x^{x}} cdot x^{x}left[(1+log x) log x+frac{1}{x}right] )