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

The answer to (\partial)/(\partial x)(x*ln(x+2y)+x/y) is ln(x+2y)+x/(x+2y)+1/y

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

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

ln (x + 2 y) + \frac{x}{x + 2 y} + \frac{1}{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

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

x \to 3 - lim (\frac{x - 3}{∣ x - 3 ∣})

(- 7) (0.3)

(2, 0), (- 2.5, 1)

\frac{d}{d x} (- 2 x^{5})

t e^{(- 3 t)} sin (5 t)

What is (\partial)/(\partial x)(x*ln(x+2y)+x/y) ?
The answer to (\partial)/(\partial x)(x*ln(x+2y)+x/y) is ln(x+2y)+x/(x+2y)+1/y