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zhannawk [14.2K]
3 years ago
5

Finding Derivatives Implicity In Exercise, find dy/dx implicity. x2 - 3 ln y + y2 = 10

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
8 0

Answer:

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

Step-by-step explanation:

We are given that

x^2-3lny+y^2=0

Differentiate w.r.t x

2x-\frac{3}{y}\frac{dy}{dx}+2y\frac{dy}{dx}=0

By using formula

\frac{dx^n}{dx}=nx^{n-1}

\frac{d(lnx)}{dx}=\frac{1}{x}

\frac{dy^n}{dx}=ny^{n-1}\frac{dy}{dx}

\frac{dy}{dx}(-\frac{3}{y}+2y)+2x=0

\frac{dy}{dx}(-\frac{3}{y}+2y)=-2x

\frac{dy}{dx}=-\frac{2x}{-\frac{3}{y}+2y}

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

Hence, the derivative of function

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

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