given the function $f(x)=e^{x + 1}$, write an expression that represents the derivative of $f$ using the…

given the function $f(x)=e^{x + 1}$, write an expression that represents the derivative of $f$ using the limit shown below. you do not have to simplify your answer. answer attempt 1 out of 2 $lim_{h\rightarrow0}$

given the function $f(x)=e^{x + 1}$, write an expression that represents the derivative of $f$ using the limit shown below. you do not have to simplify your answer. answer attempt 1 out of 2 $lim_{h\rightarrow0}$

Answer

Explanation:

Step1: Recall derivative limit definition

The derivative of a function $y = f(x)$ using the limit definition is $f'(x)=\lim_{h\rightarrow0}\frac{f(x + h)-f(x)}{h}$.

Step2: Substitute the given function

Given $f(x)=e^{x + 1}$, then $f(x + h)=e^{(x + h)+1}=e^{x+h + 1}$. So the derivative is $\lim_{h\rightarrow0}\frac{e^{x+h + 1}-e^{x + 1}}{h}$.

Answer:

$\lim_{h\rightarrow0}\frac{e^{x+h + 1}-e^{x + 1}}{h}$