A differentiable function f has f'(4) = 6. If F(x) = f(√(x)), what is F'(16)?

Chain Rule, Log Differentiation & Rate of Change · Question 24 of 130

Question 24

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A differentiable function $f$ has $f'(4) = 6$ . If $F(x) = f(\sqrt{x})$ , what is $F'(16)$ ?

\frac{3}{4}

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3

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6

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48

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CorrectNot quiteAnswer A

Correct answer: A

$F'(x) = f'(\sqrt{x}) \cdot \frac{1}{2\sqrt{x}}$ .
At 16: $\sqrt{16} = 4$ , so $F'(16) = f'(4) \cdot \frac{1}{8} = \frac{6}{8} = \frac{3}{4}$ .

Worth noting

6 is $f'(4)$ alone; the inner $\sqrt{x}$ contributes the factor $\frac{1}{2\sqrt{16}} = \frac{1}{8}$ .

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

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