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

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

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

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

4 (ln (x y) + 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 \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)

= 4 (\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}

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

Simplify

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

= 4 (ln (x y) + 1)

\int x^{11} d x

y^{^{''}} + 4 y = 1

y^{^{'}} + y = - cos (6 x)

\int x sec^{2} (3 x) d x

o f, x 2 x - 3

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