# Thread: derivative of 2(2^x)

1. ## derivative of 2(2^x)

Would it be $0(2^xln2)$ or $2(2^xln2)$

It is so confusing....

2. Originally Posted by cammywhite
Would it be $0(2^xln2)$ or $2(2^xln2)$

It is so confusing....
$2(2^xln2)$

$\frac{d(2^{x+1})}{dx} = \frac{d(2(2^x))}{dx}$

Using Chain Rule:

$= \frac{2^xd(2)}{~dx} + \frac{ 2d(2^x)}{~dx}$

= 0 +Ans
Differntiation of constant is 0 and that of the second term is your answer

3. did you mean to type $2^{2^x \ln 2}$ ?? if so, you need the chain rule. if you actually meant $2(2^x \ln 2)$, then no chain rule necessary. just note that $2 \ln 2$ is a constant, and so we just have to worry about the derivative of $2^x$, hence

$\frac d{dx} 2(2^x \ln 2) = 2 (\ln 2^2) \cdot 2^x = 2^{x + 1} (\ln 2)^2$