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Complex Plane

If y = f x 2+...

Question

If $y = f (x^{2} + 2)$ and $f^{'} (3) = 5$ , then $\frac{d y}{d x} {∣ ∣}_{x = 1}$ is

A

5

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B

25

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C

15

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D

10

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Solution

The correct option is D $10$
$\frac{d y}{d x} = f^{'} (x^{2} + 2) \times 2 x \frac{d y}{d x} {∣ ∣}_{x = 1} = f^{'} (1 + 2) \times 2 = 2 f^{'} (3) = 10$

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Similar questions

y = f (x^{2} + 2)

f^{'} (3) = 5

\frac{d y}{d x}

x = 1

y = x \sum r = 1 {tan}^{- 1} (\frac{1}{1 + r + r^{2}}),

\frac{d y}{d x}

x = 2

f (x) = \sqrt{2 x^{2} - 1}

y = f (x^{2})

\frac{d y}{d x}

x = 1

f^{'} (x) = \sqrt{2 x^{2} - 1}

y = f (x^{2})

\frac{d y}{d x}

x = 1

f^{^{'}} (x) = \sqrt{2 x^{2} - 1}

y = f (x^{2})

\frac{d y}{d x}

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