replace ? with an expression that will make the equation valid. \n\frac{d}{dx}ln(x^{5}+9)=\frac{1}{x^{5}+9}?\…

replace ? with an expression that will make the equation valid. \n\frac{d}{dx}ln(x^{5}+9)=\frac{1}{x^{5}+9}?\nthe missing expression is .

replace ? with an expression that will make the equation valid. \n\frac{d}{dx}ln(x^{5}+9)=\frac{1}{x^{5}+9}?\nthe missing expression is .

Answer

Explanation:

Step1: Apply chain - rule

The derivative of $\ln(u)$ with respect to $x$ is $\frac{1}{u}\cdot\frac{du}{dx}$ by the chain - rule. Here $u = x^{5}+9$.

Step2: Differentiate $u$

Differentiate $u=x^{5}+9$ with respect to $x$. Using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$, we have $\frac{du}{dx}=\frac{d}{dx}(x^{5}+9)=5x^{4}$.

Answer:

$5x^{4}$