Question

Differentiate f(x)=-5(12^x)

Answer 1

\[f(x)=b^x\]
\[f'(x)=b^x\times \ln(b)\]

Answer 2

Proof:

\(\large \text{let y} = b^x\)

\(\ln y = x \ln b\)

by implicit differentiation

\(\Large \frac{y'}{y} = \ln b\)

\(y' = y \lnb\)

\(\Large y' = b^x \ln b\)

Answer 3

that second to last line is \(\large y' = y \ln b\)