What is (\partial)/(\partial x)(ln(x+5y+3z)) ?

The answer to (\partial)/(\partial x)(ln(x+5y+3z)) is 1/(x+5y+3z)

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(\partial)/(\partial x)(ln(x+5y+3z))

\frac{\partial}{\partial x} (ln (x + 5 y + 3 z))

\frac{1}{x + 5 y + 3 z}

Solution steps

\frac{\partial}{\partial x} (ln (x + 5 y + 3 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x + 5 y + 3 z} \frac{\partial}{\partial x} (x + 5 y + 3 z)

= \frac{1}{x + 5 y + 3 z} \frac{\partial}{\partial x} (x + 5 y + 3 z)

\frac{\partial}{\partial x} (x + 5 y + 3 z) = 1

= \frac{1}{x + 5 y + 3 z} \cdot 1

Simplify

= \frac{1}{x + 5 y + 3 z}

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

\int_{2.5}^{0.5} (23.75 - 7.5 v) d v

\frac{\partial}{\partial y} (8 x - (x + y)^{3})

\frac{d}{d x} (\frac{1}{x ^{31}})

(\frac{2}{x} - 1)^{- 1}

What is (\partial)/(\partial x)(ln(x+5y+3z)) ?
The answer to (\partial)/(\partial x)(ln(x+5y+3z)) is 1/(x+5y+3z)