Find the derivative of this function?

Question

$y = x (x^{2} - 3)$ $y=x(x^2-3)$

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Answer 1 · 2017-01-10T05:23:45

$\frac{d y}{d x} = 3 (x^{2} - 1)$ $dy/dx=3(x^2-1)$

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

The Product Rule states that:

If $y = f (x) \cdot g (x)$ $y=f(x)*g(x)$
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:

$y=x(x^2-3)$

$= x^3-3x$

$dy/dx= 3x^2-3$

$=3(x^2-1)$