Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the derivative using logarithmic differentiation
- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Load more...
To derive the function $x^x$, use the method of logarithmic differentiation. First, assign the function to $y$, then take the natural logarithm of both sides of the equation
Apply natural logarithm to both sides of the equality
Apply logarithm properties to both sides of the equality
Derive both sides of the equality with respect to $x$
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
The derivative of the linear function is equal to $1$
The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
The derivative of the linear function is equal to $1$
The derivative of the linear function is equal to $1$
Multiply the fraction by the term $x$
Simplify the fraction
Multiply both sides of the equation by $y$
Substitute $y$ for the original function: $x^x$
The derivative of the function results in