Question

what is the derivative of 3^n

Answer 1

\[\Large y = 3^n\]
Start by taking natural log of both sides \[\Large \ln y = \ln 3^n\]
\[\Large \ln y = n \ln 3\]
Now take the power of e on both sides \[\Large e^{\ln y} =e^{ n \ln 3}\]
\[\Large y = e^ {n \ln 3}\]

now try differentiating.

Answer 2

Remember that ln3 is just a constant. If a is a constant, derivative of e^ax is a*e^ax

Answer 3

Ok got the answer: \[3^{n} \times \ln 3\]

Answer 4

thanx a lot

Answer 5

No prob. You can also get it by differentiating implicitly from this step \[\Large \ln y = n \ln 3\]
\[\Large \frac{ 1 }{ y } \times \frac{ dy }{ dx } = \ln 3 \]
\[\Large \frac{ dy }{ dx } = \ln 3 \times y = \ln 3 \times 3^n\] (since y = 3^n)

Answer 6

nice, I didn't know that we can do that, thanx again