# Derivative Product Rule

I am thinking that my error in finding this derivative is an arithmetic error,but I keep getting it wrong. I have to use Product Rule to find the solution, and only product rule.

$$f(x)=(-10x^2-7x^{\frac{2}{5}}+9)(2x^3+4)$$ For $f'(x)$ I got : $$f'(x)=(-20x-\frac{35}{2}x^{\frac{-3}{5}})(2x^3+4)+(6x^2)(-10x^2-7x^{\frac{2}{5}}+9)$$ $$f'(x)=-100x^4-77x^{\frac{12}{5}}+54x^2-40x-70x^{\frac{-3}{5}}$$

I used Product Rule to get my answer but I can't find where I made my mistake. I graphed the derivative and my answer but they don't overlap completely. What is the correct derivative of the function?

• Have a look here – Guest Nov 17 '16 at 23:52
• @Guest I've never used Wolfam Alpha before.Thanks its useful. – EnlightenedFunky Nov 17 '16 at 23:55

Deriving $7x^{\frac{2}{5}}$ should give $\frac{14}{5}x^{\frac{-3}{5}}$ and not $\frac{35}{2}x^{\frac{-3}{5}}$. You multiplied with the reciprocal of 2/5 (or divided by 2/5) instead of multiplying the exponent.