## IB Maths SL, Differentiation from first principles

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

### IB Maths SL, Differentiation from first principles

IB Mathematics SL – Derivatives, Differentiation from first principles

How can we find the first derivative function of $f(x)=3x^4$ from first principles?

Thanks
Oliver

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Joined: Mon Jan 28, 2013 8:08 pm

### IB Mathematics SL, Differentiation from first principles

IB Mathematics 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

$f'(x)=\lim_{h\to\0}\frac{3(x+h)^4-3x^4}{h}=$

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

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

$=\lim_{h\to\0}3[(x+h)+x][(x+h)^2+x^2] = 12x^3$

Thus the first derivative function is $f'(x)= 4x^3$

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

### Re: IB Maths SL, Differentiation from first principles

thank you miranda!!
Oliver

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm