Exercise 2 | Wiskunde op Tilburg University

Determine the derivative of

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

Antwoord 1 correct

Correct

Antwoord 2 optie

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

Antwoord 2 correct

Fout

Antwoord 3 optie

$y'(x) = 10x2^{5x^2+3}$ .

Antwoord 3 correct

Fout

Antwoord 4 optie

This derivative cannot be determined.

Antwoord 4 correct

Fout

Antwoord 1 optie

$y'(x) = 10\ln(2)x2^{5x^2+3}$ .

Antwoord 1 feedback

Correct: In Composite function: Exercise 1 it is shown that

$y(x)$ can be written as

$u(v(x))$ with

$v(x) = 5x^2 + 3$ and

$u(v) = 2^v$ . By the use of the chain rule we find:

$\begin{align*} v'(x) &= 5\cdot 2x + 0 = 10x\\ u'(v) &= 2^v \ln(2) = \ln(2)2^v\\ y'(x) &= u'\big(v(x)\big)\cdot v'(x) = \ln(2)2^{v(x)} \cdot 10x = 10\ln(2)x2^{5x^2+3}. \end{align*}$

Go on.

Antwoord 2 feedback

Wrong: Do not forget to multiply by

$v'(x)$ .

See Chain rule, Example 1 and Example 2.

Antwoord 3 feedback

Wrong: You probably miscalculated

$u(v) = 2^v$ :

$u'(v) \neq 2^v$ .

See Derivatives elemenatary functions.

Antwoord 4 feedback

Wrong: The derivative of

$y(x)$ can be determined by the use of the chain rule.

See Chain rule, Example 1 and Example 2.