Question

find the partial derivative with respect to v.
$\frac{partial c}{partial v}=-v + 0.0684tv$
substitute for the mean values v = 22 and t = 8 and simplify. (round your answer to four decimal places.)

Explanation:

Step1: Recall partial - derivative rule

When finding $\frac{\partial C}{\partial v}$ of $C=-v + 0.0684Tv$, treat $T$ as a constant. The derivative of $-v$ with respect to $v$ is $-1$, and the derivative of $0.0684Tv$ with respect to $v$ is $0.0684T$ (using the power - rule $\frac{d(ax)}{dx}=a$ where $a = 0.0684T$). So, $\frac{\partial C}{\partial v}=-1 + 0.0684T$.

Step2: Substitute the given values

Given $T = 8$, substitute $T$ into $\frac{\partial C}{\partial v}=-1 + 0.0684T$. Then $\frac{\partial C}{\partial v}=-1+0.0684\times8$.

Step3: Calculate the result

First, calculate $0.0684\times8 = 0.5472$. Then, $-1 + 0.5472=-0.4528$.

Answer:

$-0.4528$