What is implicit (dy)/(dx),ln(x^2-24y)=x-y-4 ?

The answer to implicit (dy)/(dx),ln(x^2-24y)=x-y-4 is (dy)/(dx)=(x^2-24y-2x)/(-24+x^2-24y)

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implicit (dy)/(dx),ln(x^2-24y)=x-y-4

implicit derivative

\frac{d y}{d x}, ln (x^{2} - 24 y) = x - y - 4

\frac{d y}{d x} = \frac{x ^{2} - 24 y - 2 x}{- 24 + x ^{2} - 24 y}

Solution steps

ln (x^{2} - 24 y) = x - y - 4

Treat

y

y (x)

Differentiate both sides:

\frac{2 x - 24 \frac{d y}{d x}}{x ^{2} - 24 y} = - \frac{d y}{d x} + 1

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{x ^{2} - 24 y - 2 x}{- 24 + x ^{2} - 24 y}

\frac{d y}{d x} = \frac{x ^{2} - 24 y - 2 x}{- 24 + x ^{2} - 24 y}

What is implicit (dy)/(dx),ln(x^2-24y)=x-y-4 ?
The answer to implicit (dy)/(dx),ln(x^2-24y)=x-y-4 is (dy)/(dx)=(x^2-24y-2x)/(-24+x^2-24y)