Exercise 2 | Wiskunde op Tilburg University

$y(x)=5^{3x^2+2}$ . Determine

$y''(x)$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$y''(x)=6\cdot 5^{3x^2+2}\cdot (1+\cdot 6 x^2)$

Antwoord 2 correct

Fout

Antwoord 3 optie

$y''(x)=5^{3x^2+2}\cdot (\textrm{ln}(5))^2$

Antwoord 3 correct

Fout

Antwoord 4 optie

$y''(x)=6\cdot 5^{3x^2+2}\cdot \textrm{ln}(5)\cdot (1+\textrm{ln}(5) \cdot x)$

Antwoord 4 correct

Fout

Antwoord 1 optie

$y''(x)=6\cdot 5^{3x^2+2}\cdot \textrm{ln}(5)\cdot (1+\textrm{ln}(5) \cdot 6 x^2)$

Antwoord 1 feedback

Correct:

$y'(x)=5^{3x^2+2}\cdot \textrm{ln}(5)\cdot 6x$ , and

$\begin{align*} y''(x) & =5^{3x^2+2}\cdot (\textrm{ln}(5))^2\cdot 6x \cdot 6x+5^{3x^2+2}\cdot \textrm{ln}(5)\cdot 6\\ & =6\cdot 5^{3x^2+2}\cdot \textrm{ln}(5)\cdot (1+\textrm{ln}(5) \cdot 6x^2). \end{align*}$

Go on.

Antwoord 2 feedback

Wrong:

$y'(x)\neq 5^{3x^2+2}\cdot 6x$ .

See Derivatives of elementary functions.

Antwoord 3 feedback

Wrong:

$y'(x) \neq 5^{3x^2+2}\cdot \textrm{ln}(5)$ .

See Chain rule.

Antwoord 4 feedback

Wrong: Do not forget the chain rule when differentiating the first-order derivative.

Try again.