Final answer to the problem
Step-by-step Solution
Specify the solving method
To derive the function $x$, 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 $x$
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 $1$
Any expression multiplied by $1$ is equal to itself
The derivative of the linear function is equal to $1$
Any expression multiplied by $1$ is equal to itself
The derivative of the linear function is equal to $1$
Any expression multiplied by $1$ is equal to itself
Multiply both sides of the equation by $y$
Any expression multiplied by $1$ is equal to itself
Substitute $y$ for the original function: $x$
Simplify the fraction $\frac{x}{x}$ by $x$
The derivative of the function results in