what is the function u? answer: $u = 2 + 4x^{2}$ what is du? answer: $8xdx$ check your variables - you might…

Explanation:

Step1: Recall the derivative rule

If $u = 2 + 4x^{2}$, by the power - rule of differentiation $\frac{d}{dx}(x^{n})=nx^{n - 1}$ and $\frac{d}{dx}(c)=0$ where $c$ is a constant.

Step2: Differentiate each term

The derivative of the constant term $2$ is $0$, and the derivative of $4x^{2}$ is $4\times2x=8x$. So, $du=\frac{du}{dx}dx$. Since $\frac{du}{dx}=8x$, then $du = 8xdx$.

Answer:

If $u = 2+4x^{2}$, then $du = 8xdx$.