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

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

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

Answer

Explanation:

Step1: Apply chain - rule

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

Step2: Differentiate $u$

Differentiate $u=x^{5}+9$ with respect to $x$. The derivative of $x^{5}$ is $5x^{4}$ and the derivative of a constant 9 is 0. So $\frac{du}{dx}=5x^{4}$.

Answer:

$5x^{4}$