Query 7.2

I've been asked how to differentiate $y=3\times2^x+1$ by someone in 7.2. Remember you can only differentiate exponential functions of the form $e^{f(x)}$. \[ y=3 \times e^{(\ln 2 \times x)}+1 \\ \frac{dy}{dx}=3\ln 2 \times e^{(\ln 2\times x)}+1 \\= 3 \ln 2 \times2^x+1 \] So when $x=0$, $\dfrac{dy}{dx}=3\ln 2 \times 2^0 +1= 3\ln 2+1=\ln 8+1=\ln {8e}$