Match each function in List I with the value of its derivative at x = 0 in List II.

Match each function in List I with the value…

Question 26

MediumOriginal question

Match each function in List I with the value of its derivative at $x = 0$ in List II.

List I	List II
A. $(1 - 3x)^{4}$	I. $4$
B. $\sqrt{1 + 8x}$	II. $-6$
C. $\tan 3x$	III. $-12$
D. $\frac{1}{(1 + 2x)^{3}}$	IV. $3$

A-II, B-I, C-IV, D-IIICorrect answerYour answerA-III, B-IV, C-I, D-IICorrect answerYour answerA-III, B-I, C-IV, D-IICorrect answerYour answerA-II, B-IV, C-I, D-IIICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A: $4(1 - 3x)^{3}(-3)$ at 0 is $-12$ . B: $\frac{8}{2\sqrt{1 + 8x}}$ at 0 is 4.
C: $3\sec^{2} 3x$ at 0 is 3. D: $-3(1 + 2x)^{-4} \cdot 2$ at 0 is $-6$ .

Worth noting

Each inner derivative ( $-3$ , 8, 3 and 2) multiplies the outer one; leaving any out changes the value.

Concept: The chain rule at a point
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe chain rule

Practise this chapter →

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Practise this chapter →

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Question 26

Explanation