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## Main Question or Discussion Point

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

- Thread starter Angus
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Do i just use the chain rule to differentiate 3^2x

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

[tex]\frac{d}{dx}a^u = a^u(\ln a)\frac{du}{dx}[/tex]

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

[tex]\frac{d}{dx}a^u = a^u(\ln a)\frac{du}{dx}[/tex]

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

Last edited:

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Gokul43201

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[tex] y=3^{2x} => ln(y)=2x*ln(3)[/tex]

Now differentiate both sides (note : ln(3) is just a constant) :

[tex] \frac {d} {dx} ln(y) = log(3)*{\frac{d} {dx}} 2x = 2*ln(3)[/tex]

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

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

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