Question

Find the derivative of the following functions using any rules.

Answer 1

We are given the following function:

`y=x^3-9x`

We are asked to determine the derivative. To do that we will take the derivative to both sides:

`(dy)/(dx)=(d)/(dx)(x^3-9x)`

Now, we distribute the derivative:

`(dy)/(dx)=(d)/(dx)(x^3)-(d)/(dx)(9x)`

For the first derivative we use the following rule:

`(d(x^n))/(dx)=nx^(n-1)`

Applying the property we get:

`(dy)/(dx)=3x^2-(d)/(dx)(9x)`

Now, we use the following rule for the final derivative:

`(d)/(dx)(ax)=a`

Applying the rule we get:

`(dy)/(dx)=3x^2-9`

Since we can't simplify it any further this is the derivative.