Question

Find the derivativef(x) = 5/x

Answer 1

`\text{f(x) = -}(5)/(x^2)`

Step-by-step explanation

We want to find the derivative of:

`f(x)\text{ = }(5)/(x)`

To do that, we have to rewrite the fraction in index form:

`f(x)=5x^(-1)`

Now, to differentiate the function with respect to x, we will mutliply the coefficient of x (5) with the power of x (-1) and then subtract 1 from its power.

That is:

`\begin{gathered} f(x)\text{ = 5 }\cdot-1(x^(-1-1)) \\ f(x)=-5x^(-2) \\ \Rightarrow\text{ f(x) = -}(5)/(x^2) \end{gathered}`