What is (\partial)/(\partial x)(ln(5x+4y)) ?

The answer to (\partial)/(\partial x)(ln(5x+4y)) is 5/(5x+4y)

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(\partial)/(\partial x)(ln(5x+4y))

\frac{\partial}{\partial x} (ln (5 x + 4 y))

\frac{5}{5 x + 4 y}

Solution steps

\frac{\partial}{\partial x} (ln (5 x + 4 y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{5 x + 4 y} \frac{\partial}{\partial x} (5 x + 4 y)

= \frac{1}{5 x + 4 y} \frac{\partial}{\partial x} (5 x + 4 y)

\frac{\partial}{\partial x} (5 x + 4 y) = 5

= \frac{1}{5 x + 4 y} \cdot 5

Simplify

\frac{1}{5 x + 4 y} \cdot 5 : \frac{5}{5 x + 4 y}

= \frac{5}{5 x + 4 y}

y = (x^{c o t (g (x))})

f (x) = 5 x

y^{^{'}} - y = 4 x - 4

\int x 1 - 4 x^{2} d x

y^{^{''}} + 25 y = sec^{2} (5 x)

What is (\partial)/(\partial x)(ln(5x+4y)) ?
The answer to (\partial)/(\partial x)(ln(5x+4y)) is 5/(5x+4y)