Question

If h(x) = squareroot 3 + 2f'(x), where f(5) = 3 and f '(5) = 2, find h'(5).

Answer 1

Answer:

h'(5) = ⅔

Step-by-step explanation:

I assume you mean h(x) = √(3 + 2f(x)).

Taking derivative using chain rule:

h'(x) = ½ (3 + 2f(x))^-½ · 2f'(x)

h'(x) = f'(x) / √(3 + 2f(x))

h'(5) = f'(5) / √(3 + 2f(5))

h'(5) = 2 / √(3 + 2 · 3)

h'(5) = ⅔

Answer 2

Chain rule of differentiation is used to find the derivative of composite functions

$h'(5) = \dfrac{2}{3}$

Reason:

Given function:

Correction $h(x) = \sqrt{3 + 2 \cdot f(x)}$

f(5) = 3

f'(5) = 2

By chain rule of differentiation, we have;

$\dfrac{dy}{dx} =\dfrac{dy}{du} \cdot \dfrac{du}{dx}$

Therefore;

$h'(x) = \dfrac{1}{2} \times (3 + 2 \cdot f(x))^{\frac{1}{2} -1} \times 2\cdot f'(x) = \dfrac{2\cdot f'(x) }{2\times \sqrt{3 + 2 \cdot f(x)} }$

$h'(x) = \dfrac{f'(x) }{ \sqrt{3 + 2 \cdot f(x)} }$

$h'(5) = \dfrac{2 }{ \sqrt{3 + 2\times 3 } } = \dfrac{2}{3}$

$h'(5) = \dfrac{2}{3}$

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