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notsponge [240]
4 years ago
10

In Exercise, find the derivative of the function. y = ln(3 + x2)

Mathematics
1 answer:
erastovalidia [21]4 years ago
5 0

Answer:  \dfrac{2x}{3 + x^2}

Step-by-step explanation:

We know the property of derivative: \dfrac{d}{dx}(\log (x))=\dfrac{1}{x}

Given function : y=\ln(3 + x^2)

Differentiate both sides with respect to x , we get

\dfrac{dy}{dx}=\dfrac{d}{dx}(\ln(3 + x^2))

\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot\dfrac{d}{dx}(3 + x^2)  [By Chain rule]

\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot(0+2x)

[Since \dfrac{d}{dx}(a)=0 , where a is scalar and \dfrac{d}{dx}(x^n)=n(x)^{n-1}]

\Rightarrow\ \dfrac{dy}{dx}=\dfrac{2x}{3 + x^2}

Hence, the derivative of the given function is \dfrac{2x}{3 + x^2} .

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