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f(x)=x^x , x in (0,oo) and let g(x) be...

`f(x)=x^x , x in (0,oo)` and let ` g(x)` be inverse of f(x) , then `g(x)'` must be

A

`x(1+log x)`

B

`x(1+ log (x))`

C

`(1)/(x(1+log g(x))`

D

non-existent

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To find \( g'(x) \) where \( g(x) \) is the inverse of the function \( f(x) = x^x \), we will follow these steps: ### Step 1: Understand the relationship between \( f(x) \) and \( g(x) \) Since \( g(x) \) is the inverse of \( f(x) \), we have: \[ f(g(x)) = x \] ...
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CENGAGE ENGLISH-DIFFERENTIATION-Execrises
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  9. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

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  13. A function f satisfies the condition f(x)=f'(x)+f''(x)+f'''(x)+…, wher...

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  14. Let f(x) be a polynomial of degree 3 such that f(3)=1, f'(3)=-1, f''(3...

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  17. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

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  18. Let y=ln (1+ cos x)^(2). The the value of (d^(2)y)/(dx^(2))+(2)/(e^(y/...

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