If `u = 3t^(4) - 5t^(3) + 2t^(2) - 18t+4`, find `(du)/(dt)` at `t = 1`.

Explanation

To find \(\frac{du}{dt}\) for the function \(u = 3t^4 - 5t^3 + 2t^2 - 18t + 4\) at \(t = 1\), we will follow these steps:

### Step 1: Differentiate the function \(u\)
We will use the power rule of differentiation, which states that \(\frac{d}{dt}(t^n) = n \cdot t^{n-1}\).

1. Differentiate \(3t^4\):
\[
\frac{d}{dt}(3t^4) = 3 \cdot 4t^{4-1} = 12t^3
...