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

1. Jun 6, 2004

Angus

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

2. Jun 6, 2004

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.

3. Jun 6, 2004

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.

Last edited: Jun 6, 2004
4. Jun 6, 2004

Gokul43201

Staff Emeritus
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 $$\frac {dy} {dx} = 3^{2x}*2ln(3)$$