1. ## Simple derivative problem

$\frac{\mathrm{d} }{\mathrm{d} x} x^2(1-2x)\\\\ x^2\frac{\mathrm{d} }{\mathrm{d} x}(1-2x) + (1-2x)\frac{\mathrm{d} }{\mathrm{d} x}x^2\\\\ x^2\frac{\mathrm{d} }{\mathrm{d} x}(1)-2\frac{\mathrm{d} }{\mathrm{d} x}(x)+(1-2x)(2x)\\\\ (x^2)(0)-2(1)+(2x-4x^2)\\\\ -4x^2+2x-2$

Something's going over my head. These are the steps when I attempt to do the problem, but the book's answer is $\frac{\mathrm{d} }{\mathrm{d} x} 2x - 6x^2$ Please and thank you.

2. ## Re: Simple derivative problem

Originally Posted by Remriel
$\frac{\mathrm{d} }{\mathrm{d} x} x^2(1-2x)\\\\ x^2\frac{\mathrm{d} }{\mathrm{d} x}(1-2x) + (1-2x)\frac{\mathrm{d} }{\mathrm{d} x}x^2\\\\ x^2\frac{\mathrm{d} }{\mathrm{d} x}(1)-2\frac{\mathrm{d} }{\mathrm{d} x}(x)+(1-2x)(2x)\\\\ (x^2)(0)-2(1)+(2x-4x^2)\\\\ -4x^2+2x-2$

Look $\displaystyle x^2(1-2x)=x^2-2x^3$ so the derivative is $\displaystyle 2x-6x^2$.

3. ## Re: Simple derivative problem

Originally Posted by Plato
Look $\displaystyle x^2(1-2x)=x^2-2x^3$ so the derivative is $\displaystyle 2x-6x^2$.
Oh, I see. Thanks! I didn't realize I had to simplify the expression before I took the derivative.

4. ## Re: Simple derivative problem

You did not. Both methods work equally well. The problem occurs in your 3rd line: you didn't distribute the x^2 to the second part. So when that evalautes to -2(1), it should actually be, -2x^2.