Exercise 4 | Wiskunde op Tilburg University

Determine the derivative of

$y(x)=\dfrac{3^{7x^3+8x}}{7x^3+8x}$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$y'(x)=\dfrac{3^{7x^3+8x}\cdot(21x^2+8)\cdot(\ln(3)-1)}{7x^3+8x}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$y'(x)=\dfrac{3^{7x^3+8x}\cdot(21x^2+8)\cdot(7x^3+8x-1)}{(7x^3+8x)^2}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$y'(x)=\dfrac{\ln(3)}{7x^3+8x}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$y'(x)=\dfrac{3^{7x^3+8x}\cdot(21x^2+8)\cdot(\ln(3)\cdot(7x^3+8x)-1)}{(7x^3+8x)^2}$

Antwoord 1 feedback

Correct:

$\begin{align} y'(x) &=\dfrac{(21x^2+8)\ln(3)3^{7x^3+8x}\cdot(7x^3+8x)-(21x^2+8)3^{7x^3+8x}}{(7x^3+8x)^2}\\ & = \dfrac{3^{7x^3+8x}\cdot(21x^2+8)\cdot(\ln(3)\cdot(7x^3+8x)-1)}{(7x^3+8x)^2}. \end{align}$

Go on.

Antwoord 2 feedback

Wrong: In general

$\dfrac{a+b}{b^2}$ is not equal to

$\dfrac{a}{b}$ .

Try again.

Antwoord 3 feedback

Wrong: The derivative of

$3^x$ is not

$3^x$ .

See Derivatives elementary functions.

Antwoord 4 feedback

Wrong: In general

$a\cdot b \cdot c - a \cdot c$ is not equal to

$b$ .

Try again.