Question

question find $\frac{dy}{dx}$ if $y = (-5x^{4}-4)^{3}$. provide your answer below: $\frac{dy}{dx}=square$

Explanation:

Step1: Apply chain - rule

Let $u=-5x^{4}-4$, then $y = u^{3}$. The chain - rule states that $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. First, find $\frac{dy}{du}$ and $\frac{du}{dx}$.
For $y = u^{3}$, $\frac{dy}{du}=3u^{2}$.
For $u=-5x^{4}-4$, $\frac{du}{dx}=-20x^{3}$.

Step2: Calculate $\frac{dy}{dx}$

Substitute $u=-5x^{4}-4$ into $\frac{dy}{du}$ and multiply by $\frac{du}{dx}$:
$\frac{dy}{dx}=3(-5x^{4}-4)^{2}\cdot(-20x^{3})=-60x^{3}(-5x^{4}-4)^{2}$.

Answer:

$-60x^{3}(-5x^{4}-4)^{2}$