Resolved: "Find dydx in xy = x+y"

arenceabigns

Answered question

2021-06-05

Find

\frac{d y}{d x}

in xy = x+y

Nola Robson

Skilled2021-06-06Added 94 answers

Step 1
We have to find

\frac{d y}{d x}

in the given equation:
xy=x+y
We know the formula of derivatives,

\frac{d x^{n}}{d x} = n x^{n - 1}

\frac{d (u v)}{d x} = u \frac{d v}{d x} + v \frac{d u}{d x}

Step 2
Applying above formula for the given equation, we get

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

x \frac{d y}{d x} + y \frac{d x}{d x} = 1 + \frac{d y}{d x}

x \frac{d y}{d x} + y \times 1 = 1 + \frac{d y}{d x}

x \frac{d y}{d x} - \frac{d y}{d x} = 1 - y

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

\frac{d y}{d x} = \frac{1 - y}{x - 1}

Hence, value of

\frac{d y}{d x} i s \frac{1 - y}{x - 1}

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