find f(x). f(x)=(5 - 3x)^9 f(x)=

Explanation:

Step1: Identify the outer - inner functions

Let $u = 5-3x$, then $y = u^{9}$.

Step2: Differentiate the outer function

The derivative of $y$ with respect to $u$ is $\frac{dy}{du}=9u^{8}$ (using the power rule $\frac{d}{du}(u^{n})=nu^{n - 1}$ with $n = 9$).

Step3: Differentiate the inner function

The derivative of $u$ with respect to $x$ is $\frac{du}{dx}=-3$ (since $\frac{d}{dx}(5 - 3x)=\frac{d}{dx}(5)-3\frac{d}{dx}(x)=0 - 3=-3$).

Step4: Apply the chain - rule

By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substitute $\frac{dy}{du}=9u^{8}$ and $\frac{du}{dx}=-3$ into the chain - rule formula, and replace $u$ with $5 - 3x$. So $\frac{dy}{dx}=9(5 - 3x)^{8}\cdot(-3)$.

Answer:

$-27(5 - 3x)^{8}$