1. Calculate the following derivatives explicitly: \[ f(x) = \log_3(x) + 3^{x} \qquad \qquad g(x) = \log_3(2x-1) + 3^{x^2} \] \[ h(x) = \log_3(2x-1) \times 3^{x^2} \]
2. Calculate the following integrals explicitly: \[ \int \frac{7}{6x+5} \,\mathrm{d}x \qquad \int 2^t\,\mathrm{d}t \qquad \int \sec^2(t)4^{\tan(t)}\,\mathrm{d}t \]