Question

question 9. 1 point determine r(x) if r(x)=(4^x)^6. select the correct answer below: r(x)=(6x)4^(6x - 1) r(x)=4^x(6ln4) r(x)=6(4^x) r(x)=4^x(4ln6) r(x)=6(4^x)^5

Explanation:

Step1: Use power - rule for differentiation

If $y = u^n$, then $y^\prime=nu^{n - 1}u^\prime$. Here $u = 4^x$ and $n = 6$. First, find the derivative of $u = 4^x$. The derivative of $a^x$ is $a^x\ln a$, so $u^\prime=4^x\ln 4$.

Step2: Calculate $r^\prime(x)$

$r(x)=(4^x)^6$, so $r^\prime(x)=6(4^x)^5\times4^x\ln 4=6(4^x)^6\ln 4$.

Answer:

$r^\prime(x)=6(4^x)^6\ln 4$