Hello, this problem states to differentiate the expression with respect to q. I am not sure of the steps taken to get the final result.
This is an economics problem differentiating the variable cost function to get the marginal cost function.
Hello, this problem states to differentiate the expression with respect to q. I am not sure of the steps taken to get the final result.
This is an economics problem differentiating the variable cost function to get the marginal cost function.
So you want to differentiate:
$\displaystyle 6(\frac{q}{10k^{0.4}})^{1.67}$ with respect to q?
In which case, we have:
$\displaystyle 6\frac{q^{1.67}}{(10k^{0.4})^{1.67}}$
=$\displaystyle \frac{6q^{1.67}}{(10k^{0.4})^{1.67}}$
But the $\displaystyle \frac{6}{(10k^{0.4})^{1.67}}$(everything except the $\displaystyle q^{1.67}$) is just constant. It's a stable value, like 4 or 7 - it isn't a variable.
For the sake of simplicity, I'm going to let $\displaystyle \frac{6}{(10k^{0.4})^{1.67}}=c$
When we differentiate $\displaystyle 4x^n$ with respect to $\displaystyle x$, we get: $\displaystyle 4nx^{n-1}$.
When we differentiate $\displaystyle ax^n$ with respect to $\displaystyle x$, we get: $\displaystyle anx^{n-1}$
We have: $\displaystyle c\times~q^{1.67}$
So, differentiating, we get: $\displaystyle 1.67c\times~q^{0.67}$
Then, slipping c back in as $\displaystyle \frac{6}{(10k^{0.4})^{1.67}}$, we have:
$\displaystyle \frac{1.67\times~6\times~q^{0.67}}{(10k^{0.4})^{1. 67}}$
and $\displaystyle 1.67\times~6=10.02$ which is where that number arises.