Question

Would the derivative of
\[f(x) = x ^{3}(5x-2)^{2}\] be
\[(x ^{2}(5x-2))(25x-6)\]?

Answer 1

I would first exapand \(f(x)\) to make things a little easier:
\[f(x)=x^3(5x-2)^2=x^3(25x^2-20x+4)=25x^5-20x^4+4x^3\]
So then the derivative would be:
\[f'(x)=125x^4-80x^3+12x^2\]

Now you ended up with:
\[f'(x)=x^2(5x-2)(25x-6)\]
We can simplify:
\[f'(x)=x^2(125x^2-30x-50x+12)=125x^4-80x^3+12x^2\]
So in conclusion, YES! Haha

Answer 2

thank you! :)

Answer 3

No prob Jigglypuff!