If f(x) = (x^2 + 1)^3, what is f'(1)?

Derivatives & Second-Order Derivatives · Question 10 of 96

Question 10

MediumOriginal question

If $f(x) = \left(x^{2} + 1\right)^{3}$ , what is $f'(1)$ ?

8

Correct answerYour answer

12

Correct answerYour answer

24

Correct answerYour answer

48

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

By the chain rule, $f'(x) = 3(x^2 + 1)^2 \cdot 2x = 6 x \left(x^{2} + 1\right)^{2}$ .
At $x = 1$ : $6(1)(2)^2 = 24$ .

Worth noting

8 is $f(1)$ , the value of the function itself; 12 forgets the inner factor $2x$ .

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.