Question

assignment submission for this assignment, you submit answers by question. assignment scoring your last submission is used for your score. 1. -/1 points 0/100 submissions used find the derivative of the function. f(x)=(9 - x)^5 f(x)= resources read it watch it

Explanation:

Step1: Identify the outer - inner functions

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

Step2: Differentiate the outer function

The derivative of $y$ with respect to $u$, $\frac{dy}{du}=5u^{4}$.

Step3: Differentiate the inner function

The derivative of $u$ with respect to $x$, $\frac{du}{dx}=- 1$.

Step4: Apply the chain - rule

By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substitute $\frac{dy}{du}=5u^{4}$ and $\frac{du}{dx}=-1$ into the chain - rule formula. Since $u = 9 - x$, we have $\frac{dy}{dx}=5(9 - x)^{4}\cdot(-1)=-5(9 - x)^{4}$.

Answer:

$-5(9 - x)^{4}$