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:

$\frac{dy}{dx}=\frac{d}{dx}(x^3-9x)$

Now, we distribute the derivative:

$\frac{dy}{dx}=\frac{d}{dx}(x^3)-\frac{d}{dx}(9x)$

For the first derivative we use the following rule:

$\frac{d(x^n)}{dx}=nx^{n-1}$

Applying the property we get:

$\frac{dy}{dx}=3x^2-\frac{d}{dx}(9x)$

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

$\frac{d}{dx}(ax)=a$

Applying the rule we get:

$\frac{dy}{dx}=3x^2-9$

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