If f(x) = x√(x + 3), what is f'(1)?

Derivatives & Second-Order Derivatives · Question 25 of 96

Question 25

MediumOriginal question

If $f(x) = x\sqrt{x + 3}$ , what is $f'(1)$ ?

\frac{1}{4}

Correct answerYour answer

2

Correct answerYour answer

\frac{9}{4}

Correct answerYour answer

\frac{5}{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Product rule: $f'(x) = \sqrt{x + 3} + x \cdot \frac{1}{2\sqrt{x + 3}}$ .
At $x = 1$ : $\sqrt{4} + \frac{1}{2 \times 2} = 2 + \frac{1}{4} = \frac{9}{4}$ .

Worth noting

$\frac{1}{4}$ keeps only $x$ times the derivative of the root and drops the term $\sqrt{x + 3}$ .

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

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