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  • Find dy/dx when x and y are connected by the relation given tan-1 (x2 + y2) = a

Find \frac{dy}{dx} when x and y are connected by the relation given tan^{-1} (x^2 + y^2) = a
 

Answers (1)

We have,

tan^{-1} (x^2 + y^2) = a

x^2 + y^2 = tan a

On differentiating both sides with respect to x, we get

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

Posted by

infoexpert22

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