Question

If sec[(x+y)/(x-y)]=a. Prove that dy/dx = (y/x)

Answer 1

$\frac{x + y}{x - y} = {sec}^{ - 1} a$
differenciate with respect to x by
quotient rule

$\frac{(x - y)(1 + \frac{dy}{dx} ) - (x + y)(1 - \frac{dy}{dx} )}{ {(x - y)}^{2} } = 0$

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

Answer 2

dy/dx = y/x  if Sec((x-y)/(x + y)) = a

Step-by-step explanation:

Sec((x-y)/(x + y)) = a

(x-y)/(x + y)  = Sec⁻¹(a)

Differentiating wrt x

=> (x - y) ( - 1/(x + y)²)(1 + dy/dx)    + (1 - dy/dx)/(x + y) = 0

multiplying by (x + y)²

=> (y - x)(1 + dy/dx)  + (1 - dy/dx)(x + y)  = 0

=> y  +  ydy/dx  - x  - xdy/dx  + x - xdy/dx  + y - ydy/dx  = 0

=>  2y = 2xdy/dx

=> dy/dx = 2y/2x

=> dy/dx = y/x

Learn more:

(x + 3)^{2} .(x + 4)^{3} .(x + 5)^{4} प्रदत्त फलनों का x के सापेक्ष अवकलन कीजिए

brainly.in/question/15287089

f(x) = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) द्वारा प्रदत्त फलन का अवकलज ज्ञात कीजिए और इस प्रकार f'(1) ज्ञात कीजिए।