find the indicated derivative.\n$\frac{d}{dx}\frac{15x + 36}{x}$\n$\frac{d}{dx}\frac{15x + 36}{x}=square$
find the indicated derivative.\n$\frac{d}{dx}\frac{15x + 36}{x}$\n$\frac{d}{dx}\frac{15x + 36}{x}=square$
Answer
Explanation:
Step1: Simplify the function
First, rewrite $\frac{15x + 36}{x}$ as $15+\frac{36}{x}=15 + 36x^{-1}$.
Step2: Apply the power - rule for derivatives
The derivative of a constant $C$ is $0$, and the derivative of $x^n$ with respect to $x$ is $nx^{n - 1}$. The derivative of $15$ is $0$, and the derivative of $36x^{-1}$ is $36\times(-1)x^{-1 - 1}=-36x^{-2}$.
Step3: Combine the results
The derivative of $15 + 36x^{-1}$ is $0-36x^{-2}=-\frac{36}{x^{2}}$.
Answer:
$-\frac{36}{x^{2}}$