Calculate $\frac{d y}{d x}$. You need not expand your answer.
\[
\frac{y=\left(3 x^{2}+x\right)\left(x-x^{2}\right)}{d x}=\square
\]
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Answer
So, the derivative of the function \(y=(3x^2+x)(x-x^2)\) is \(\boxed{(1 - 2x)(3x^2 + x) + (6x + 1)(-x^2 + x)}\).
Step 1 ：Given the function \(y=(3x^2+x)(x-x^2)\).
Step 2 ：We need to find the derivative of this function.
Step 3 ：We can use the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
Step 4 ：Applying the product rule, we get \((1 - 2x)(3x^2 + x) + (6x + 1)(-x^2 + x)\).
Step 5 ：So, the derivative of the function \(y=(3x^2+x)(x-x^2)\) is \(\boxed{(1 - 2x)(3x^2 + x) + (6x + 1)(-x^2 + x)}\).
