(Solved):   DEFINITION OF DIFFERENTIATION \[ f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{ ...

 

DEFINITION OF DIFFERENTIATION \[ f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \] Find \( f^{\prime}(x) \) using the definition of the derivative for a) \( f(x)=2 x^{2}+3 x \) c) \( f(x)=\frac{3}{x+6} \) QUESTION 2 \begin{tabular}{l} RULES OF DifFERENTIATION \\ 1. Product rule \\ \( \frac{d}{d x}(f(x) g(x))=g(x) r^{r}(x)+f(x) g^{\prime}(x) \) \\ 2. Quobent ule \\ \( \frac{d}{d x}\left(\frac{f(x)}{g(x)}\right)=\frac{g(x) f(x)-f(x) g^{\prime}(x)}{(g(x))^{2}} \) \\ 3. Power rule \\ \( \frac{d}{d x}(f(x))^{n}=n[f(x))^{r^{-1}} f(x) \) \\ 4. Chain nule \\ \( \frac{d}{d x} f(g(x))=f(g(x)) g^{\prime \prime}(x) \) \\ \hline \end{tabular} Find \( f^{\prime} x \) using the appropriate formula: d) \( f(x)=\frac{3 x-6}{x^{2}+3 x-7} \)