# What is the equation of the line tangent to # f(x)=x^(1/x)# at # x=1#?

To find the tangent's slope just derivate the function.

We have

So take the log of both sides,

Derivate both sides,

To find the slope at

We know all lines follow the equation

We know

So the tangent line is

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The equation of the line tangent to f(x)=x^(1/x) at x=1 is y = 1.

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