Differentiate the following w.r.t x.(i) `sqrt(3x+2)+(1/(sqrt(2x^2 + 4)))` (ii) `e^(sec^2(x))+3cos^-1(x)` (iii) `log_7(logx)`

Explanation

Let's solve the given differentiation problems step by step.

### Part (i): Differentiate \( \sqrt{3x + 2} + \frac{1}{\sqrt{2x^2 + 4}} \)

1. **Rewrite the expression**:
\[ y = (3x + 2)^{1/2} + (2x^2 + 4)^{-1/2} \]
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