## Derivatives IB Math Studies

Number and algebra, Descriptive statistics, Logic, sets and probability, Statistical applications, Geometry and trigonometry, Mathematical models, Introduction to differential calculus.

### Derivatives IB Math Studies

IB Mathematical Studies SL – Calculus, Derivatives, Differentiation from first principles

How can we find the first derivative function of $f(x)=x^3$ from first principles?

Thanks
hill

Posts: 0
Joined: Tue Mar 19, 2013 8:49 pm

### Re: Derivatives IB Math Studies

IB Mathematical Studies SL – Calculus, Derivatives, Differentiation from first principles

We know that the definition of the first derivative function is given by the following formula:

$f'(x)=\lim_{h\to\0}\frac{f(x+h)-f(x)}{h}$

So in our case, we have the following

$f'(x)=\lim_{h\to\0}\frac{(x+h)^3-x^3}{h}=$

$=\lim_{h\to\0}\frac{x^3+3hx^2+3xh^2+h^3-x^3}{h}=$

$=\lim_{h\to\0}\frac{h(3x^2+3xh+h^2)}{h}=$

$=\lim_{h\to\0}(3x^2+3xh+h^2) = 3x^2$

Thus the first derivative function is $f'(x)= 3x^2$

Hope these help!!
elizabeth

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Joined: Mon Jan 28, 2013 8:09 pm

### Re: Derivatives IB Math Studies

Thanks Elisabeth!!
hill

Posts: 0
Joined: Tue Mar 19, 2013 8:49 pm