Question

let (f(x)= - 4sin(x)-9ln(x)+11). (f(x)=square)

Explanation:

Step1: Recall derivative rules

Use sum - difference rule of derivatives $\frac{d}{dx}(u\pm v\pm w)=\frac{du}{dx}\pm\frac{dv}{dx}\pm\frac{dw}{dx}$, derivative of $\sin(x)$ is $\cos(x)$ and derivative of $\ln(x)$ is $\frac{1}{x}$, and derivative of a constant is 0.

Step2: Differentiate each term

For $y = - 4\sin(x)-9\ln(x)+11$, we have $\frac{d}{dx}(-4\sin(x))=-4\cos(x)$, $\frac{d}{dx}(-9\ln(x))=-\frac{9}{x}$, and $\frac{d}{dx}(11) = 0$.

Step3: Combine the derivatives

$f'(x)=-4\cos(x)-\frac{9}{x}$.

Answer:

$-4\cos(x)-\frac{9}{x}$