Question

hw10 differentiation rules 1 (targets c1, c5; §3.3) due: mon oct 6, 2025 11:59pm
attempt 1 in progress
details
no additional details were added for this assignment.
hw10 differentiation rules 1 (targets c1, c5; §3.3) score: 8/9 answered: 8/9
question 9
if (f(x)=5ln(x)+\frac{3}{x}), find (f(x)).
question help: message instructor
submit question

Explanation:

Step1: Recall derivative rules

The derivative of $\ln(x)$ is $\frac{1}{x}$ and the derivative of $x^n$ is $nx^{n - 1}$. For the function $f(x)=5\ln(x)+\frac{3}{x}=5\ln(x)+3x^{- 1}$.

Step2: Differentiate term - by - term

The derivative of $5\ln(x)$ using the constant multiple rule ($(cf(x))'=cf'(x)$) is $5\times\frac{1}{x}=\frac{5}{x}$. The derivative of $3x^{-1}$ using the power rule is $3\times(-1)x^{-1 - 1}=-3x^{-2}=-\frac{3}{x^{2}}$.

Step3: Combine the derivatives

$f'(x)=\frac{5}{x}-\frac{3}{x^{2}}$.

Answer:

$f'(x)=\frac{5}{x}-\frac{3}{x^{2}}$