What is (\partial)/(\partial x)(ln(3x+2y)) ?

The answer to (\partial)/(\partial x)(ln(3x+2y)) is 3/(3x+2y)

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(\partial)/(\partial x)(ln(3x+2y))

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

\frac{3}{3 x + 2 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{3 x + 2 y} \frac{\partial}{\partial x} (3 x + 2 y)

= \frac{1}{3 x + 2 y} \frac{\partial}{\partial x} (3 x + 2 y)

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

= \frac{1}{3 x + 2 y} \cdot 3

Simplify

\frac{1}{3 x + 2 y} \cdot 3 : \frac{3}{3 x + 2 y}

= \frac{3}{3 x + 2 y}

\frac{d}{d x} (ln (x^{3} - 63))

f (t) = cos (π t)

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\int_{- 3}^{3} \frac{x}{1 + ∣ x ∣} d x

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

What is (\partial)/(\partial x)(ln(3x+2y)) ?
The answer to (\partial)/(\partial x)(ln(3x+2y)) is 3/(3x+2y)