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}
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