Question

antiderivative of 6^x ?

Answer 1

since ex and ln(x) are inverse functions, x= e^ln(x) for all x.
\[6^x= e^{\ln(6^x)}= e^{x \ln(6)} \]
so that
\[ \frac{d(6^x)}{dx}= \frac{de^{x \ln(6)}}{dx}= \ln(6) 6^x\]
\[Since \frac{d(6^x)}{dx}= \ln(6) 6^x\]
the anti-derivative of 6^x is (1/ln(6)) 6^x.