given the function $f(x)=x^{5}$, write an expression that represents the derivative of $f$ using the limit…

given the function $f(x)=x^{5}$, 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 $lim_{h\rightarrow0}square$ submit answer

given the function $f(x)=x^{5}$, 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 $lim_{h\rightarrow0}square$ submit answer

Answer

Explanation:

Step1: Recall the limit - definition of the derivative

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

Step2: Substitute $f(x)=x^{5}$ into the formula

We know that $f(x + h)=(x + h)^{5}$ and $f(x)=x^{5}$. So the derivative $f^\prime(x)=\lim_{h\rightarrow0}\frac{(x + h)^{5}-x^{5}}{h}$.

Answer:

$\lim_{h\rightarrow0}\frac{(x + h)^{5}-x^{5}}{h}$