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derivative of x^2ln(x^3)

Solution

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

Solution

6 x ln (x) + 3 x

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = ln (x^{3})

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

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

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

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

Simplify

2 x ln (x^{3}) + \frac{3}{x} x^{2} : 6 x ln (x) + 3 x

= 6 x ln (x) + 3 x

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\frac{d}{d x} (e^{6})

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Frequently Asked Questions (FAQ)

What is the derivative of x^2ln(x^3) ?
The derivative of x^2ln(x^3) is 6xln(x)+3x
What is the first derivative of x^2ln(x^3) ?
The first derivative of x^2ln(x^3) is 6xln(x)+3x