Exercise 1 | Wiskunde op Tilburg University

Determine which of the following functions is an antiderivative of

$f(x)=e^{2x}+\frac{1}{\sqrt{x}}$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$F(x)=e^{2x}+\frac{1}{x\sqrt{x}}+3$

Antwoord 2 correct

Fout

Antwoord 3 optie

$F(x)=\frac{1}{2}e^{2x}+\sqrt{x}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$F(x)=e^{2x}+2\sqrt{x}-x$

Antwoord 4 correct

Fout

Antwoord 1 optie

$F(x)=\frac{1}{2}e^{2x}+2\sqrt{x}-10$

Antwoord 1 feedback

Correct.

$F(x)$ is an antiderivative of

$f(x)$ , because

$F(x)'=f(x)$ .

Go on.

Antwoord 2 feedback

Wrong. Note that

$(e^{2x})'\not=e^{2x}$ .

See Chain rule.

Antwoord 3 feedback

Wrong. Note that

$(\sqrt{x})'\not=\frac{1}{\sqrt{x}}$ .

See Derivatives of elementary functions.

Antwoord 4 feedback

Wrong. Pay attention to the final term

$-x$ .

Try again.