# Are these two equivalent

When finding derivatives, a useful tool is $$(a^x)' = (a^x)ln(a)$$. Now say I have $$2^{3x}$$. When trying to find the derivative, are these two equivalent? $$(2^x)ln(2)(3)$$ and $$(3x)2^{3x - 1}$$

They are not equivalent, the first derivative is given by $$(2^{3x})'=2^{3x}\ln(2)\cdot 3$$ by the chain rule.
• Since $$(a^x)'=a^x\ln(a)$$ and your case is $$a=2$$ – Dr. Sonnhard Graubner Dec 10 '18 at 17:29
Both $$(2^x)ln(2)(3)$$ and $$(3x)2^{3x - 1}$$ are wrong !
We have $$2^{3x}=8^x$$, hence $$(2^{3x})'=8^x \ln (8).$$
• So was the rule taught to me incorrect? $( a x ) ′ =( a x )ln(a)$ – ming Dec 10 '18 at 17:58