Question

$\small{ \boxed{ \bold{\red{\: \:\: if \: y = \sin ^ { - 1 } [ \frac { 5 x + 12 \sqrt { 1 - x ^ { 2 } } } { 13 } ] \: find \: \frac{dy}{dx} .}}}}$
Answer with proper explanation.


Don't spam.


→ Expecting answer from :

★ Moderators
★ Brainly stars and teacher
★ Others best users ​​

Answer 1

Hope this❀(*´▽`*)❀ answer

l

Answer 2

Answer:

$y = sin {}^{ - 1} ( \frac{5x + 12 \sqrt{1} - x {}^{2} }{ 13} )$

$Let x=sinθ</p><p></p><p>$

$y = {sin}^{ - 1} ( \frac{5sinθ + 12cosθ}{13} )</p><p></p><p>$

${sin}^{ - 1} ( \frac{5}{13}sinθ + \frac{12}{13} cosθ)$

∴y=sin−¹(sin θ cos α+sin α cos θ)

[/tex]

where α= {tan}^{ - 1} ( \frac{12}{5} )[/tex]

=sin−¹ sin (θ+α) = θ+α

∴y=sin−¹ x+α

$∴ \frac{dy}{dx} = \frac{1}{ \sqrt{1 - {x}^{2} } }$

Hope this helps you

Mark as brainliest