Find fracdydx of the following. y2 - x2 = cos(xy), x2 = frac9y2. | Basic Mathematics 2079

Basic Mathematics20795 marksNumerical: implicit differentiationImplicit differentiation

Find $\frac{dy}{dx}$ of the following. $y^2 - x^2 = \cos(xy)$ , $x^2 = \frac{9}{y^2}$ . [5]

Find $\frac{dy}{dx}$ of the following. $y^2 - x^2 = \cos(xy)$, $x^2 = \frac{9}{y^2}$. [5]

Equation 1: $y^2 - x^2 = \cos(xy)$ - Equation 2: $x^2 = \dfrac{9}{y^2}$ Find $\dfrac{dy}{dx}$ for each (implicit differentiation). --- Differentiate both sides with respect to $x$ : $\frac{d}{dx}(y^2 - x^2) = \frac{d}{dx}[\cos(xy)]$ Left side: $2y\frac{dy}{dx} - 2x$ Right side (chain rule + ...

Equation 1: $y^2 - x^2 = \cos(xy)$ - Equation 2: $x^2 = \dfrac{9}{y^2}$ Find $\dfrac{dy}{dx}$ for each (implicit differentiation). --- Differentiate both sides with respect to $x$: $$\frac{d}{dx}(y^2 - x^2) = \frac{d}{dx}[\cos(xy)]$$ Left side: $$2y\frac{dy}{dx} - 2x$$ Right side (chain rule + ...