Find the derivative of this function?

y=x(x^2-3)

1 Answer
Jan 10, 2017

dy/dx=3(x^2-1)

Explanation:

Since this is problem in the Product Rule section we will apply it here;

The Product Rule states that:

If y=f(x)*g(x)
Then dy/dx = f(x)*g'(x) + f'(x)*g(x)

In our example:

f(x) = x and g(x) = (x^2-3)

Hence: dy/dx= x*2x + 1*(x^2-3)

= 2x^2+x^2-3

=3(x^2-1)

Note however that this problem is more simply solved by first expanding the expression and applying the Power Rule as follows:

y=x(x^2-3)

= x^3-3x

dy/dx= 3x^2-3

=3(x^2-1)