Exercise 3 | Wiskunde op Tilburg University

Determine the derivative of

$y(x)=e^{x+\ln(x)}$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$y'(x)=e^{x+\ln(x)}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$y'(x)=e^{1+\frac{1}{x}}$

Antwoord 3 correct

Fout

Antwoord 4 optie

None of the other answers is correct.

Antwoord 4 correct

Fout

Antwoord 1 optie

$y'(x)=(1+x)e^x$

Antwoord 1 feedback

Correct:

$\begin{align*} y'(x) & = e^{x+\ln(x)}\cdot(1+\frac{1}{x})\\ & = e^x\cdot e^{\ln{x}}\cdot(1+\frac{1}{x})\\ & = e^x \cdot x \cdot (1+\frac{1}{x})\\ & = e^x (1+x). \end{align*}$

Go on.

Antwoord 2 feedback

Wrong: Do not forget the chain rule.

See Chain rule.

Antwoord 3 feedback

Wrong: The chain rule does not state the following.

Let

$y(x) = u(v(x))$ be a composite function. Then:

$y'(x) = u'(v'(x)).$

See Chain rule.

Antwoord 4 feedback

Wrong: The correct answer is among them.

Try again.