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  3. Chapter 2: Differentiation of functions of one variable
  4. Chain rule
  5. Chain rule
  6. Exercise 1

Exercise 1

Determine the derivative of $f(x)=(x^2+3)^2+3$.
$f'(x)=4x^3+12x$
$f'(x)=2x(x^2+3)$
$f'(x)=2x(x^2+3)+3$
$f'(x)=4x(x^2+3)+3$
Determine the derivative of $f(x)=(x^2+3)^2+3$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$f'(x)=2x(x^2+3)$
Antwoord 2 correct
Fout
Antwoord 3 optie
$f'(x)=2x(x^2+3)+3$
Antwoord 3 correct
Fout
Antwoord 4 optie
$f'(x)=4x(x^2+3)+3$
Antwoord 4 correct
Fout
Antwoord 1 optie
$f'(x)=4x^3+12x$
Antwoord 1 feedback
Correct: $$\begin{align*}
f'(x) & = 2(x^2+3)\cdot 2x\\
& = 4x^3+12x.
\end{align*}$$

Go on.
Antwoord 2 feedback
Wrong: Do not forget the outside square.

See Chain rule.
Antwoord 3 feedback
Wrong: What is the derivative of 3?

Try again.
Antwoord 4 feedback
Wrong: What is the derivative of 3?

Try again.