What is (\partial)/(\partial x)(2xln(x^2y)) ?

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

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(\partial)/(\partial x)(2xln(x^2y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

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

- \frac{2}{s ^{2}}

\int 5 x lo g_{10} (3 - x) d x

x, 0, 1

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

\frac{d}{d x} (5 x^{3})

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