What is (\partial)/(\partial x)(ln(x+6y+8z)) ?

The answer to (\partial)/(\partial x)(ln(x+6y+8z)) is 1/(x+6y+8z)

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(\partial)/(\partial x)(ln(x+6y+8z))

\frac{\partial}{\partial x} (ln (x + 6 y + 8 z))

\frac{1}{x + 6 y + 8 z}

Solution steps

\frac{\partial}{\partial x} (ln (x + 6 y + 8 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x + 6 y + 8 z} \frac{\partial}{\partial x} (x + 6 y + 8 z)

= \frac{1}{x + 6 y + 8 z} \frac{\partial}{\partial x} (x + 6 y + 8 z)

\frac{\partial}{\partial x} (x + 6 y + 8 z) = 1

= \frac{1}{x + 6 y + 8 z} \cdot 1

Simplify

= \frac{1}{x + 6 y + 8 z}

\frac{d y}{d x} = - \frac{2}{x ^{3}} + 2 e^{2 x - 2}

f (x) = 2 x^{2} + 5 x^{2} - 2, at x = 2

y = x^{2} + 6

\int_{- 1}^{1} x^{3} - x d x

\int \frac{sin ^{2} ( x )}{4} d x

What is (\partial)/(\partial x)(ln(x+6y+8z)) ?
The answer to (\partial)/(\partial x)(ln(x+6y+8z)) is 1/(x+6y+8z)