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  3. Chapter 2: Differentiation of functions of one variable
  4. Rules of differentiation
  5. Diagnostic exercises differentiation
  6. Exercise 4

Exercise 4

Consider the function $f(x)=\ln(x)+\frac{1}{x}$. Determine $f'(3)$.
$\frac{2}{9}$
$\frac{4}{9}$
$-\frac{1}{6}$
$\ln(3)+\frac{1}{3}$
Consider the function $f(x)=\ln(x)+\frac{1}{x}$. Determine $f'(3)$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$\frac{4}{9}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$-\frac{1}{6}$
Antwoord 3 correct
Fout
Antwoord 4 optie
$\ln(3)+\frac{1}{3}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$\frac{2}{9}$
Antwoord 1 feedback
Correct: $f'(x)=\frac{1}{x}-\frac{1}{x^2}$.

$f'(0)=\frac{1}{3}-\frac{1}{9}=\frac{2}{9}$.

Go on.
Antwoord 2 feedback
Wrong: The derivative of $\frac{1}{x}$ is not $\frac{1}{x^2}$.

See Derivatives elementary functions.
Antwoord 3 feedback
Wrong: $\frac{1}{3}-\frac{1}{9} \neq \frac{1}{6}$.

Try again.
Antwoord 4 feedback
Wrong: The question is not to determine $f(3)$.

Try again.