Question

How do you find the derivative of the function `R=3W^(2*pi)` at `W=7`?

Answer 1

`[(dR)/(dW)]_(W=7) = (6pi)/7 * 7^(2pi`

Explanation:

We have:

`R=3W^(2pi)`

If we differentiate `R` wrt `W` using the power rule, we get:

`(dR)/(dW) = 3(2pi)W^(2pi-1)`
`\ \ \ \ \ \ \ = 6pi \ W^(2pi-1)`

So when `W=7` we have:

`[(dR)/(dW)]_(W=7) = 6pi (7^(2pi-1))`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = (6pi)/7 * 7^(2pi`