What is (\partial)/(\partial x)(ln(8x+7y)) ?

The answer to (\partial)/(\partial x)(ln(8x+7y)) is 8/(8x+7y)

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(\partial)/(\partial x)(ln(8x+7y))

\frac{\partial}{\partial x} (ln (8 x + 7 y))

\frac{8}{8 x + 7 y}

Solution steps

\frac{\partial}{\partial x} (ln (8 x + 7 y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{8 x + 7 y} \frac{\partial}{\partial x} (8 x + 7 y)

= \frac{1}{8 x + 7 y} \frac{\partial}{\partial x} (8 x + 7 y)

\frac{\partial}{\partial x} (8 x + 7 y) = 8

= \frac{1}{8 x + 7 y} \cdot 8

Simplify

\frac{1}{8 x + 7 y} \cdot 8 : \frac{8}{8 x + 7 y}

= \frac{8}{8 x + 7 y}

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = x e^{x}

\int_{1}^{5} \frac{x}{x ^{2} + 6 x + 13} d x

\int \frac{1}{1 + e ^{12 x}} d x

(7, 0), (- 1, 2)

e^{- (t - 3)^{2}}

What is (\partial)/(\partial x)(ln(8x+7y)) ?
The answer to (\partial)/(\partial x)(ln(8x+7y)) is 8/(8x+7y)