What is (\partial)/(\partial x)(4xln(x)y) ?

The answer to (\partial)/(\partial x)(4xln(x)y) is 4y(ln(x)+1)

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(\partial)/(\partial x)(4xln(x)y)

\frac{\partial}{\partial x} (4 x ln (x) y)

4 y (ln (x) + 1)

Solution steps

\frac{\partial}{\partial x} (4 x ln (x) y)

Treat

y

as a constant

Take the constant out:

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

= 4 y \frac{\partial}{\partial x} (x ln (x))

Apply the Product Rule:

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

f = x, g = ln (x)

= 4 y (\frac{\partial}{\partial x} (x) ln (x) + \frac{\partial}{\partial x} (ln (x)) x)

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

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

= 4 y (1 \cdot ln (x) + \frac{1}{x} x)

Simplify

4 y (1 \cdot ln (x) + \frac{1}{x} x) : 4 y (ln (x) + 1)

= 4 y (ln (x) + 1)

What is (\partial)/(\partial x)(4xln(x)y) ?
The answer to (\partial)/(\partial x)(4xln(x)y) is 4y(ln(x)+1)