What is (\partial)/(\partial x)(4ln(x+z)) ?

The answer to (\partial)/(\partial x)(4ln(x+z)) is 4/(x+z)

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(\partial)/(\partial x)(4ln(x+z))

\frac{\partial}{\partial x} (4 ln (x + z))

\frac{4}{x + z}

Solution steps

\frac{\partial}{\partial x} (4 ln (x + z))

Treat

z

as a constant

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{x + z} \frac{\partial}{\partial x} (x + z)

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

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

= 4 \cdot \frac{1}{x + z} \cdot 1

Simplify

4 \cdot \frac{1}{x + z} \cdot 1 : \frac{4}{x + z}

= \frac{4}{x + z}

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y^{^{''}} + 12 y^{^{'}} + 85 y = 0

What is (\partial)/(\partial x)(4ln(x+z)) ?
The answer to (\partial)/(\partial x)(4ln(x+z)) is 4/(x+z)