What is ln(xy)+(y+x(dy)/(dx))/y ?

The solution to ln(xy)+(y+x(dy)/(dx))/y is ln(x)+ln(y)+(y+x(dy)/(dx))/y

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simplify ln(xy)+(y+x(dy)/(dx))/y

simplify

ln (x y) + \frac{y + x \frac{d y}{d x}}{y}

ln (x) + ln (y) + \frac{y + x \frac{d y}{d x}}{y}

Solution steps

ln (x y) + \frac{y + x \frac{d y}{d x}}{y}

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x y) = ln (x) + ln (y)

= ln (x) + ln (y) + \frac{x \frac{d y}{d x} + y}{y}

lo g_{10} (5 e^{9})

4 lo g_{3} (x) - \frac{1}{2} lo g_{3} (y) + 2 lo g_{3} (z)

1 - ln (2 e)

- \frac{3}{2 ^{44} \cdot 5 ^{44}} ln (10)

\frac{π}{e ^{3} \cdot ln ( 20 )}

What is ln(xy)+(y+x(dy)/(dx))/y ?
The solution to ln(xy)+(y+x(dy)/(dx))/y is ln(x)+ln(y)+(y+x(dy)/(dx))/y