What is (\partial)/(\partial x)(3xln(xy)) ?

The answer to (\partial)/(\partial x)(3xln(xy)) is 3(ln(xy)+1)

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(\partial)/(\partial x)(3xln(xy))

\frac{\partial}{\partial x} (3 x ln (x y))

3 (ln (x y) + 1)

Solution steps

\frac{\partial}{\partial x} (3 x ln (x y))

Treat

y

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (x ln (x y))

Apply the Product Rule:

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

f = x, g = ln (x y)

= 3 (\frac{\partial}{\partial x} (x) ln (x y) + \frac{\partial}{\partial x} (ln (x y)) x)

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

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

= 3 (1 \cdot ln (x y) + \frac{1}{x} x)

Simplify

3 (1 \cdot ln (x y) + \frac{1}{x} x) : 3 (ln (x y) + 1)

= 3 (ln (x y) + 1)

\frac{\partial}{\partial x} ((x^{3} + x^{4}) (x^{2} + 3 x)^{2})

\int_{1}^{4} (5 x^{3} - 6) d x

\frac{d y}{d x} = 5 y e^{x + 8}

\int sec^{3} (7 x) d x

y^{^{'}} = sec (2) (x - y)

What is (\partial)/(\partial x)(3xln(xy)) ?
The answer to (\partial)/(\partial x)(3xln(xy)) is 3(ln(xy)+1)