- #1
Fairy111
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Homework Statement
Find the derivative of the following function f.
Homework Equations
f(x)=x^log(x)
The Attempt at a Solution
I really don't know how to do this, as it's x to the power of a function of x.
The formula for differentiating f(x)=x^log(x) is f'(x) = (ln(x) + 1)x^log(x).
Yes, f(x)=x^log(x) can be simplified to f(x) = x^(1+log(x)).
To differentiate f(x)=x^log(x) using the product rule, you would use the formula f'(x) = u'v + uv', where u = x and v = x^log(x). This would give you the final result of f'(x) = (ln(x) + 1)x^log(x).
The domain of f(x)=x^log(x) is all positive real numbers.
The range of f(x)=x^log(x) is all positive real numbers.