What is the derivative of (x^2*ln(x)) ?

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

What is the first derivative of (x^2*ln(x)) ?

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

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

2 x ln (x) + x

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

\frac{1}{x} x^{2} = x

= 2 x ln (x) + x

f (x) = \frac{x ^{2}}{9 + 2 x}

\int_{0}^{1} π (x - x^{10}) d x

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

4 x^{3} - 12 x^{2}

\frac{d}{d x} (e^{7 x - 4})

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