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  3. Chapter 2: Differentiation of functions of one variable
  4. Chain rule
  5. Chain rule
  6. Exercise 4

Exercise 4

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