What is (\partial)/(\partial x)(ln(4x+7y+3z)) ?

The answer to (\partial)/(\partial x)(ln(4x+7y+3z)) is 4/(4x+7y+3z)

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(\partial)/(\partial x)(ln(4x+7y+3z))

\frac{\partial}{\partial x} (ln (4 x + 7 y + 3 z))

\frac{4}{4 x + 7 y + 3 z}

Solution steps

\frac{\partial}{\partial x} (ln (4 x + 7 y + 3 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{4 x + 7 y + 3 z} \frac{\partial}{\partial x} (4 x + 7 y + 3 z)

= \frac{1}{4 x + 7 y + 3 z} \frac{\partial}{\partial x} (4 x + 7 y + 3 z)

\frac{\partial}{\partial x} (4 x + 7 y + 3 z) = 4

= \frac{1}{4 x + 7 y + 3 z} \cdot 4

Simplify

\frac{1}{4 x + 7 y + 3 z} \cdot 4 : \frac{4}{4 x + 7 y + 3 z}

= \frac{4}{4 x + 7 y + 3 z}

\frac{d}{d x} (2 cos (x) + 2 sin (x))

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

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

\frac{d}{d x} (9^{2})

What is (\partial)/(\partial x)(ln(4x+7y+3z)) ?
The answer to (\partial)/(\partial x)(ln(4x+7y+3z)) is 4/(4x+7y+3z)