What is the derivative of y+x(ln(x-ln(y)-1)) ?

The derivative of y+x(ln(x-ln(y)-1)) is (dy}{dx}-(x\frac{dy)/(dx))/y+ln(x)-ln(y)

What is the first derivative of y+x(ln(x-ln(y)-1)) ?

The first derivative of y+x(ln(x-ln(y)-1)) is (dy}{dx}-(x\frac{dy)/(dx))/y+ln(x)-ln(y)

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\frac{d}{d x} (y + x (ln (x) - ln (y) - 1))

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

Solution steps

\frac{d}{d x} (y + x (ln (x) - ln (y) - 1))

Apply the Sum/Difference Rule:

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

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

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

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

\int 4 x - 5 d x

\frac{s ^{3}}{s + 2}

\frac{d}{d x} (ln (2 x - y))

\int_{0}^{1} 5 d x

y^{^{'}} = e^{2 y}, y (0) = 0

What is the derivative of y+x(ln(x-ln(y)-1)) ?
The derivative of y+x(ln(x-ln(y)-1)) is (dy}{dx}-(x\frac{dy)/(dx))/y+ln(x)-ln(y)
What is the first derivative of y+x(ln(x-ln(y)-1)) ?
The first derivative of y+x(ln(x-ln(y)-1)) is (dy}{dx}-(x\frac{dy)/(dx))/y+ln(x)-ln(y)