Question

hw_3.1_the chain rule
due sunday by 11:59pm points 100.75 submitting
hw_3.1_the chain rule

1. submit answer practice similar

attempt 1: 10 attempts remaining.
calculate the derivative of the function.
f(x)=(3x - 1)^2
f(x)=

Explanation:

Step1: Identify inner and outer functions

Let $u = 3x - 1$, so $f(x)=u^{2}$.

Step2: Differentiate outer function with respect to u

The derivative of $y = u^{2}$ with respect to $u$ is $\frac{dy}{du}=2u$.

Step3: Differentiate inner function with respect to x

The derivative of $u = 3x - 1$ with respect to $x$ is $\frac{du}{dx}=3$.

Step4: Apply chain - rule

By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substitute $u = 3x - 1$, $\frac{dy}{du}=2u$ and $\frac{du}{dx}=3$ into the chain - rule formula. We get $\frac{dy}{dx}=2u\cdot3=2(3x - 1)\cdot3$.

Step5: Simplify the result

$2(3x - 1)\cdot3 = 6(3x - 1)=18x-6$.

Answer:

$18x - 6$