Using Product rule, find the derivatives of the following functions: (i) y = (3x2+2)(5x−3). (ii) y = ex sin x. (iii) y = log x.

Let $u = 3x^2 + 2$ and $v = 5x - 3$.

$u' = \frac{d}{dx}(3x^2 + 2) = 6x$
$v' = \frac{d}{dx}(5x - 3) = 5$

The derivative is $\boxed{\mathbf{45x^2 - 18x + 10}}$.

Let $u = e^{2x}$ and $v = \sin x$.

$u' = \frac{d}{dx}(e^{2x}) = 2e^{2x}$
$v' = \frac{d}{dx}(\sin x) = \cos x$

The derivative is $\boxed{\mathbf{e^{2x}(2\sin x + \cos x)}}$.

Let $u = e^{2x}$ and $v = \log x$.

$u' = \frac{d}{dx}(e^{2x}) = 2e^{2x}$
$v' = \frac{d}{dx}(\log x) = \frac{1}{x}$

The derivative is $\boxed{\mathbf{e^{2x}\left(2\log x + \frac{1}{x}\right)}}$.