What is the derivative of 2^x, 3^x?

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What is the derivative of 2^x, 3^x?

The derivative of e^x = e^x...

thank you in advance
 
Let y = 2<sup>x</sup>, so ln(y) = x ln(2).

Differentiate.

Solve for "(dy/dx)=".

Plug "2<sup>x</sup>" in for "y", and simplify to find dy/dx.

Eliz.
 
Re: Thanks Liz...you are always helpful...

americo74 said:
ChaoticLlama said:
What's the matter? stapel gave you the answer.
For some reason, "americo74" likes to hide much of his posts in the "Subject" line. This has frequently led to confusion.... :?

Eliz.
 
stapel said:
Let y = 2<sup>x</sup>
...or...\(\displaystyle \L\;2^{x}\;=\;[e^{ln(2)}]^{x}\;=\;e^{xln(2)}\)

The derivative of the last expressions, remembering the chain rule, gives the desired result.
 
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