A "Tricky" Derivative

Calculus Level 2

Suppose that $f(x)=x^{x^{x}}$ . Find the derivative of $f(x)$ with respect to $x$ .

x^{x^{x}}(x^{x}\ln(x^{x})+x^{x^{x}})

x^{x^{x}}(x^{x}\ln x(1+\ln x)+x^{x-1})

x^{x^{x-1}}-\ln x+x^{x}

x^{x^{x}}(x+\ln x)+1

1 solution

Eros Roess
Aug 25, 2019

Hint: You can use this substitution: $a=e^{ln(a)}$

You need to put a backslash in front of all functions in LaTex \ln x $\ln x$ . Note that "ln" is not in italic but "x" is. Because ln is a function and x is a variable. Also there is a space between ln and x. Note that if you enter ln x $ln x$ , the whole thing is in italic and there is no space in between.

Chew-Seong Cheong - 1 year, 9 months ago

Thanks for the tip. I'm still new to this.

Eros Roess - 1 year, 9 months ago

A "Tricky" Derivative

1 solution

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