Differentiate with respect to x : sin-1 { x2 / root under x4 + a4 } The answer: - Maths - Continuity and Differentiability

Question

Differentiate with respect to x :

sin-1 { x2 / root under x4 +
a4 }

The answer: 2a2 x / ( a4 + x4 )

Manbar Singh · Accepted Answer

Let y = sin-1x2x4 + a4put x2 = a2 tan θNow, y = sin-1a2 tan θa4 tan2θ + a4⇒y = sin-1a2 tan θa4tan2θ + 1⇒y = sin-1a2 tan θa2sec2θ⇒y = sin-1tan θsec θ⇒y = sin-1 sin θ⇒y = θ⇒y = tan-1x2a2⇒dydx = 11 + x4a4 × 2xa2⇒dydx = a4a4 + x4 × 2xa2⇒dydx = 2a2xa4 + x4

Differentiate with respect to x : sin-1 { x2 / root under x4 + a4 } The answer: 2a2 x / ( a4 + x4 )

Differentiate with respect to x :

sin^-1 { x² / root under x⁴ + a⁴ }

The answer: 2a² x / ( a⁴ + x⁴ )