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

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

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

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

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derivative of

f (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

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