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Derivative of 2^x

What is the Derivative of 2^x?

The derivative of 2^x is 2^x\ln(2).

Solution. Let f(x) = 2^x. We have seen here that:
\begin{align*}
\frac{d}{dx} a^x = a^x \ln(a). 
\end{align*}
Now, in our case, we have that a = 2. So substituting that in above, we get:
\begin{align*}
f'(x) = 2^x \ln(2). 
\end{align*}
Therefore, the derivative of 2^x is 2^x\ln(2).

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