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Popular >

derivative of xln^2(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (y+3/y)(y^2-5)derivative of

(y + \frac{3}{y}) (y^{2} - 5)

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\frac{d}{d x} (sec^{n - 2} (x))

limit as x approaches 0 of (10^x-1)/x

x \to 0 lim (\frac{1 0 ^{x} - 1}{x})

derivative of (x^4+2)^2(x^5+4)^4 derivative of

(x^{4} + 2)^{2} (x^{5} + 4)^{4}

derivative of x^2-2x+5 derivative of

x^{2} - 2 x + 5

Frequently Asked Questions (FAQ)

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