replace ? with an expression that will make the equation valid. \n\frac{d}{dx}(7 - 5x^{2})^{8}=8(7…

Explanation:

Step1: Apply chain - rule

The chain - rule states that if $y = u^n$ and $u$ is a function of $x$, then $\frac{dy}{dx}=n\cdot u^{n - 1}\cdot\frac{du}{dx}$. Here, $u = 7-5x^{2}$ and $n = 8$. We know that $\frac{d}{dx}(7 - 5x^{2})^{8}=8(7 - 5x^{2})^{7}\cdot\frac{d}{dx}(7 - 5x^{2})$.

Step2: Differentiate $7-5x^{2}$

Using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$ and $\frac{d}{dx}(c)=0$ (where $c$ is a constant), we have $\frac{d}{dx}(7 - 5x^{2})=\frac{d}{dx}(7)-\frac{d}{dx}(5x^{2})=0-10x=- 10x$.

Answer:

$-10x$