What is the derivative of ln((x-b^2)-ln((y-a)^2)) ?

The derivative of ln((x-b^2)-ln((y-a)^2)) is 2/(x-b)-(2\frac{dy)/(dx)}{y-a}

What is the first derivative of ln((x-b^2)-ln((y-a)^2)) ?

The first derivative of ln((x-b^2)-ln((y-a)^2)) is 2/(x-b)-(2\frac{dy)/(dx)}{y-a}

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

\frac{2}{x - b} - \frac{2 \frac{d y}{d x}}{y - a}

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln ((x - b)^{2})) - \frac{d}{d x} (ln ((y - a)^{2}))

\frac{d}{d x} (ln ((x - b)^{2})) = \frac{2}{x - b}

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

= \frac{2}{x - b} - \frac{2 \frac{d y}{d x}}{y - a}

f (x) = x^{2} - 4 x + 9

e^{x} - y^{2}

\frac{d}{d t} (10 + 5 t)

\frac{2000}{x}

\frac{( x ^{2} + 2 x )}{( x + 1 )}

What is the derivative of ln((x-b^2)-ln((y-a)^2)) ?
The derivative of ln((x-b^2)-ln((y-a)^2)) is 2/(x-b)-(2\frac{dy)/(dx)}{y-a}
What is the first derivative of ln((x-b^2)-ln((y-a)^2)) ?
The first derivative of ln((x-b^2)-ln((y-a)^2)) is 2/(x-b)-(2\frac{dy)/(dx)}{y-a}