What is the derivative of the function \( f(x)=\frac{\ln x}{\ln x-1} \) ? Select one: a. \( \frac{1}{x(\ln x-1)^{2}} \) b. \( \frac{1}{\ln x(\ln x-1)^{2}} \) c. \( \frac{-1}{x(\ln x-1)^{2}} \) d. \( \frac{1}{x(\ln x-1)^{2}} \)

Differentiate. (Hint: Use the Extended Power Rule.) \( g(x)=(\ln x)^{4} \)

Differentiate. \( F(x)=\frac{1}{9 x-7} \)

Find the general form of \( f \) if \( f^{\prime}(x)=8 f(x) \).

On considère la fonction numérique \( f \) définie par: \[ f(x)=x-\sqrt{3-x^{2}} \] 1. Determiner \( D f \). \( \forall x \in D_{f} \quad f(x) \geq-2 \sqrt{3} \). 2. Montrer que : \( -2 \sqrt{3} \) est - il la valeur minimale de \( f \) sur \( D_{f} \).

Given the following function, determine the difference quotient, \( \frac{f(x+h)-f(x)}{h} \) \[ f(x)=x^{2}-7 x+3 \] Answer