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Popular >

derivative of xln(x^2+5)

Solution

\frac{d}{d x} (x ln (x^{2} + 5))

Solution

ln (x^{2} + 5) + \frac{2 x ^{2}}{x ^{2} + 5}

Solution steps

\frac{d}{d x} (x ln (x^{2} + 5))

Apply the Product Rule:

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

f = x, g = ln (x^{2} + 5)

= \frac{d x}{d x} ln (x^{2} + 5) + \frac{d}{d x} (ln (x^{2} + 5)) x

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

\frac{d}{d x} (ln (x^{2} + 5)) = \frac{2 x}{x ^{2} + 5}

= 1 \cdot ln (x^{2} + 5) + \frac{2 x}{x ^{2} + 5} x

Simplify

1 \cdot ln (x^{2} + 5) + \frac{2 x}{x ^{2} + 5} x : ln (x^{2} + 5) + \frac{2 x ^{2}}{x ^{2} + 5}

= ln (x^{2} + 5) + \frac{2 x ^{2}}{x ^{2} + 5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of xln(x^2+5) ?
The derivative of xln(x^2+5) is ln(x^2+5)+(2x^2)/(x^2+5)
What is the first derivative of xln(x^2+5) ?
The first derivative of xln(x^2+5) is ln(x^2+5)+(2x^2)/(x^2+5)