What is the derivative of xln(x^2+2) ?

The derivative of xln(x^2+2) is ln(x^2+2)+(2x^2)/(x^2+2)

What is the first derivative of xln(x^2+2) ?

The first derivative of xln(x^2+2) is ln(x^2+2)+(2x^2)/(x^2+2)

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derivative of

x ln (x^{2} + 2)

ln (x^{2} + 2) + \frac{2 x ^{2}}{x ^{2} + 2}

Solution steps

\frac{d}{d x} (x ln (x^{2} + 2))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x^{2} + 2)

= \frac{d x}{d x} ln (x^{2} + 2) + \frac{d}{d x} (ln (x^{2} + 2)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (x^{2} + 2)) = \frac{2 x}{x ^{2} + 2}

= 1 \cdot ln (x^{2} + 2) + \frac{2 x}{x ^{2} + 2} x

Simplify

1 \cdot ln (x^{2} + 2) + \frac{2 x}{x ^{2} + 2} x : ln (x^{2} + 2) + \frac{2 x ^{2}}{x ^{2} + 2}

= ln (x^{2} + 2) + \frac{2 x ^{2}}{x ^{2} + 2}

\frac{d}{d y} ((y - 1)^{2})

x \to 0 - lim (x e^{\frac{2}{x}})

\int_{0}^{2} x e^{- x^{2}} d x

\int_{0}^{\frac{3 π}{2}} ∣ cos (x) ∣ d x

f (x) = \frac{2}{2 x + 1}

What is the derivative of xln(x^2+2) ?
The derivative of xln(x^2+2) is ln(x^2+2)+(2x^2)/(x^2+2)
What is the first derivative of xln(x^2+2) ?
The first derivative of xln(x^2+2) is ln(x^2+2)+(2x^2)/(x^2+2)