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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 + lim (e^{- 2 x} ln (x))

\frac{1}{x}, 3

\frac{1}{2} x y

6 x + \frac{16}{3}

\frac{\partial}{\partial x} (2 sin (2 x))

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