Question

1. - / 1 points 0/100 submissions used

find the derivative of the function.
f(x) = 9(x^3 - x)^4
f(x) =
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Explanation:

Step1: Identify outer - inner functions

Let $u = x^{3}-x$ and $y = 9u^{4}$.

Step2: Find derivative of outer function

The derivative of $y$ with respect to $u$ is $\frac{dy}{du}=9\times4u^{3}=36u^{3}$.

Step3: Find derivative of inner function

The derivative of $u$ with respect to $x$ is $\frac{du}{dx}=3x^{2}-1$.

Step4: Apply chain - rule

By the chain - rule $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substitute $u = x^{3}-x$ back in: $f^{\prime}(x)=36(x^{3}-x)^{3}(3x^{2}-1)$.

Answer:

$36(3x^{2}-1)(x^{3}-x)^{3}$