hw_3.1_the chain rule\ndue sunday by 11:59pm points 100.75 submitting an ex\nhw_3.1_the chain rule\n14…

Explanation:

Step1: Identify inner - outer functions

Let $u = 0.2x^{2}-4.4x + 2.1$ and $y = u^{2.1}$.

Step2: Differentiate outer function

The derivative of $y$ with respect to $u$ using the power rule $\frac{d}{du}(u^{n})=nu^{n - 1}$ is $\frac{dy}{du}=2.1u^{1.1}$.

Step3: Differentiate inner function

The derivative of $u$ with respect to $x$ is $\frac{du}{dx}=(0.2\times2x-4.4)=0.4x - 4.4$.

Step4: Apply chain rule

By the chain rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$, we substitute $u = 0.2x^{2}-4.4x + 2.1$ back in. So $r^{\prime}(x)=2.1(0.2x^{2}-4.4x + 2.1)^{1.1}(0.4x - 4.4)$.

Answer:

$2.1(0.2x^{2}-4.4x + 2.1)^{1.1}(0.4x - 4.4)$