Question

find f(x).
f(x)=(3 - 9x)^{14}
f(x)=\square

Explanation:

Step1: Apply the chain rule

Let \(u = 3-9x\), then \(f(x)=u^{14}\). The chain rule states that \(\frac{df}{dx}=\frac{df}{du}\cdot\frac{du}{dx}\).
First, find \(\frac{df}{du}\):
If \(f(u) = u^{14}\), then \(\frac{df}{du}=14u^{13}\) (using the power rule \(\frac{d}{du}(u^n)=nu^{n - 1}\)).

Step2: Find \(\frac{du}{dx}\)

If \(u=3 - 9x\), then \(\frac{du}{dx}=-9\) (since \(\frac{d}{dx}(a+bx)=b\), here \(a = 3\) and \(b=-9\)).

Step3: Substitute back

Substitute \(u = 3-9x\) into \(\frac{df}{du}\) and use the chain - rule formula \(\frac{df}{dx}=\frac{df}{du}\cdot\frac{du}{dx}\).
\(\frac{df}{dx}=14(3 - 9x)^{13}\cdot(-9)\)

Answer:

\(-126(3 - 9x)^{13}\)