What is (\partial)/(\partial x)(x^2ln(x)) ?

The answer to (\partial)/(\partial x)(x^2ln(x)) is 2xln(x)+x

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(\partial)/(\partial x)(x^2ln(x))

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

2 x ln (x) + x

Solution steps

\frac{\partial}{\partial 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{\partial}{\partial x} (x^{2}) ln (x) + \frac{\partial}{\partial x} (ln (x)) x^{2}

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

\frac{\partial}{\partial 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

\int \frac{4 x - 2}{( x ^{2} - x + 1 ) ^{7}} d x

f (x) = ln (cos (2 x))

\int \frac{8}{16 - x ^{2}} d x

y = 7 - x, x = \frac{( y - 4 ) ^{2}}{4}

\int (2 x + 1) e^{x} d x

What is (\partial)/(\partial x)(x^2ln(x)) ?
The answer to (\partial)/(\partial x)(x^2ln(x)) is 2xln(x)+x