Question

x^24y^14=(x+y)^40 find dy/dx​

Answer 1

Answer:

$\frac{dy}{dx} = \frac{y(16x - 24y)}{x(14x - 26y)}$

Step-by-step explanation:

${x}^{24} {y}^{14} = (x + y)^{2} \\Differentiating \: \: with \: \: respect \: \: to \: \: X \\ {x}^{24}.14 {y}^{13}. \frac{dy}{dx} + 24 {x}^{23}. {y}^{14} = 40(x + y) ^{39}.(1 + \frac{dy}{dx} ) \\ {x}^{24}. {y}^{14} ( \frac{14}{y} . \frac{dy}{dx} + \frac{24}{x} ) = 40(x + y) ^{39}.(1 + \frac{dy}{dx} ) \\ (x + y)^{40}( \frac{14}{y} . \frac{dy}{dx} + \frac{24}{x} ) = 40(x + y) ^{39} .(1 + \frac{dy}{dx} ) \\ (x + y)( \frac{14}{y} . \frac{dy}{dx} + \frac{24}{x} ) = 40(1 + \frac{dy}{dx} ) \\ \frac{14x}{y}. \frac{dy}{dx} + 24 + 14 .\frac{dy}{dx} + \frac{24y}{x} = 40 + 40. \frac{dy}{dx} \\ \frac{14x}{y}. \frac{dy}{dx} + 14 .\frac{dy}{dx} - 40. \frac{dy}{dx} =40 - 24 - \frac{24y}{x} \\ \frac{dy}{dx}( \frac{14x}{y} - 26) = 16 - \frac{24y}{x} \\ \frac{dy}{dx}( \frac{14x - 26y}{y} ) = \frac{16x - 24y}{x} \\ \frac{dy}{dx} = \frac{16x - 24y}{x} \times \frac{y}{14x - 26y} \\ \frac{dy}{dx} = \frac{y(16x - 24y)}{x(14x - 26y)}$