Question

find f(x). f(x)=(1 - 2x)^9 f(x)=□

Explanation:

Step1: Identify the outer - inner functions

Let $u = 1 - 2x$, then $y = u^{9}$.

Step2: Differentiate the outer function

The derivative of $y$ with respect to $u$, $\frac{dy}{du}=9u^{8}$.

Step3: Differentiate the inner function

The derivative of $u$ with respect to $x$, $\frac{du}{dx}=-2$.

Step4: Apply the chain - rule

By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substitute $u = 1 - 2x$, $\frac{dy}{du}=9u^{8}$ and $\frac{du}{dx}=-2$ into the chain - rule formula. We get $\frac{dy}{dx}=9(1 - 2x)^{8}\cdot(-2)$.

Answer:

$-18(1 - 2x)^{8}$