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  3. Chapter 2: Differentiation of functions of one variable
  4. Rules of differentiation
  5. Diagnostic exercises differentiation
  6. Exercise 1

Exercise 1

Determine the derivative of $f(x)=(x+3)(x-1)(x-5)$.
$f'(x)=3x^2-6x-13$
$f'(x)=3x^2-10x-25$
$f'(x)=x^3-2x^2-19x+20$
$f'(x)=3x^2-4x-19$.
Determine the derivative of $f(x)=(x+3)(x-1)(x-5)$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$f'(x)=3x^2-10x-25$
Antwoord 2 correct
Fout
Antwoord 3 optie
$f'(x)=x^3-2x^2-19x+20$
Antwoord 3 correct
Fout
Antwoord 4 optie
$f'(x)=3x^2-4x-19$.
Antwoord 4 correct
Fout
Antwoord 1 optie
$f'(x)=3x^2-6x-13$
Antwoord 1 feedback
Correct: $f(x)=(x+3)(x-1)(x-5)=(x^2+2x-3)(x-5)=x^3-3x^2-13x+15$.

$f'(x)=3x^2-6x-13$.

Go on.
Antwoord 2 feedback
Wrong: $f'(x)\neq (x-1)(x-5)+(x+3)(x-5)+(x+3)(x-5)$.

See Product rule (film).
Antwoord 3 feedback
Wrong: $f'(x)\neq (x-1)(x-5)+(x+3)\cdot\Big((x-5)\cdot (x-1)\Big)$.

See Product rule (film).
Antwoord 4 feedback
Wrong: $f(x)\neq (x-1)(x-5)+(x+3)\cdot\Big((x-5)\cdot (x-1)\Big)$.

See Product rule (film).