Question

x²/4 - y²/9=1,Find dy/dx.

Answer 1

$\underline{\large{\text{Answer}}}:\\ \\ \text {Given that,}\\ \\ \frac{{\text {x}}^{2}}{4}-\frac { {\text {y}}^{2}}{9}=1\\ \\ \to 9 {\text {x}}^{2}-4 {\text {y}}^{2}=36 \\ \\ \text {Now, differentiating both sides w. r. to x, we get} \\ \\ \frac {\text {d}}{\text {dx}}(9 {\text {x}}^{2}-4 {\text {y}}^{2})=\frac{\text {d}}{{\text {dx}}}(36) \\ \\ \to 9\frac {\text {d}}{\text {dx}}({\text {x}}^{2})-4\frac {\text {d}}{\text {dx}}({\text {y}}^{2})=0 \\ \\ \to \text {9 (2x)}-\text {4 (2y)}\frac {\text {dy}}{\text {dx}}=0 \\ \\ \to \text {9x}-\text {4y}\frac {\text {dy}}{\text {dx}}=0 \\ \\ \to \text {4y}\frac {\text {dy}}{\text {dx}}=\text {9x} \\ \\ \to \frac {\text {dy}}{\text {dx}}=\frac {\text {9x}}{\text {4y}} \\ \\ \therefore \boxed {\frac {\text {dy}}{\text {dx}}=\frac {\text {9x}}{\text {4y}}} \\ \\ \bigstar \underline {\large {\text {MarkAsBrainliest}}}\bigstar$

Answer 2

$\underline{Hey\: mate!}$

differentiate w.r.t. x

Note

$\\\\derivative\\\\\boxed{\implies x^{n}=n x^{n-1}}$

$\\\\\\ \frac{2x^{1}}{4} - \frac{2y^{1}}{9}\frac{dy}{dx} =0 \\ \\\\\frac{x}{2} - \frac{2y^{1}}{9}\frac{dy}{dx}=0\\ \\\\\frac{dy}{dx}=\frac{x}{2}.\frac{9}{2y}\\\\\\\boxed{\implies \frac{dy}{dx}=\frac{9x}{4y}}$

$\underline{Answer}$