Do i just use the chain rule to differentiate 3^2x

[Angus]

Do i just use the chain rule to differentiate 3^2x

 

[Muzza]

Is that 3^{2x}? If so, yes, you can use the chain rule, or you could write it as (3^2)^x = 9^x and differentiate that instead.

 

[TALewis]

You might not know the chain rule for forms a^u. I certainly didn't encounter it a lot. Use this:

\frac{d}{dx}a^u = a^u(\ln a)\frac{du}{dx}

a is a constant. u is a function of x.

 

[Gokul43201]

Or you can do the following
y=3^{2x} => ln(y)=2x*ln(3)
Now differentiate both sides (note : ln(3) is just a constant) :
\frac {d} {dx} ln(y) = log(3)*{\frac{d} {dx}} 2x = 2*ln(3)

But \frac {d} {dx} ln(y) =\frac{1} {y} \frac {dy} {dx} = \frac {1} {3^{2x}} \frac {dy} {dx}

So \frac {dy} {dx} = 3^{2x}*2ln(3)