Question

differentiate $f(x)=log_2(1 - 9x)$. $f(x)=$ attempt 1: 2 attempts remaining. submit answer next item

Explanation:

Step1: Recall the derivative formula for $\log_a(u)$

The derivative of $\log_a(u)$ with respect to $x$ is $\frac{1}{u\ln(a)}\cdot\frac{du}{dx}$, where $u = 1 - 9x$ and $a = 2$.

Step2: Identify $u$ and $\frac{du}{dx}$

Here $u=1 - 9x$, so $\frac{du}{dx}=-9$.

Step3: Apply the formula

$f'(x)=\frac{1}{(1 - 9x)\ln(2)}\cdot(-9)=-\frac{9}{(1 - 9x)\ln(2)}$.

Answer:

$-\frac{9}{(1 - 9x)\ln(2)}$