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Popular >

derivative of xln^3(x)

Solution

\frac{d}{d x} (x ln^{3} (x))

Solution

ln^{3} (x) + 3 ln^{2} (x)

Solution steps

\frac{d}{d x} (x ln^{3} (x))

Apply the Product Rule:

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

f = x, g = ln^{3} (x)

= \frac{d x}{d x} ln^{3} (x) + \frac{d}{d x} (ln^{3} (x)) x

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

\frac{d}{d x} (ln^{3} (x)) = \frac{3 ln ^{2} ( x )}{x}

= 1 \cdot ln^{3} (x) + \frac{3 ln ^{2} ( x )}{x} x

Simplify

1 \cdot ln^{3} (x) + \frac{3 ln ^{2} ( x )}{x} x : ln^{3} (x) + 3 ln^{2} (x)

= ln^{3} (x) + 3 ln^{2} (x)

Popular Examples

limit as x approaches 0 of sin(kx)

x \to 0 lim (sin (k x))

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\int \frac{11 x ^{3}}{9 + x ^{2}} d x

derivative of (x^3/4-3x)

\frac{d}{d x} (\frac{x ^{3}}{4} - 3 x)

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\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{1}{4 x})

Frequently Asked Questions (FAQ)

What is the derivative of xln^3(x) ?
The derivative of xln^3(x) is ln^3(x)+3ln^2(x)
What is the first derivative of xln^3(x) ?
The first derivative of xln^3(x) is ln^3(x)+3ln^2(x)