Find dervatives of the following functions:
(i) `y=2x^(3)` , (ii) `y=4/x` , (iii) `y=3e^(x)` , (iv) `y=6 ln x` , (v) `y=5 sin x`

Explanation

To find the derivatives of the given functions, we will apply the basic rules of differentiation. Let's solve each function step by step.

### Step 1: Differentiate \( y = 2x^3 \)
To differentiate \( y = 2x^3 \):
- Use the power rule: \( \frac{d}{dx}(x^n) = n \cdot x^{n-1} \).
- Here, \( n = 3 \), so:
\[
\frac{dy}{dx} = 2 \cdot 3x^{3-1} = 6x^2
...