prove that d/dx( x/2 (a2 -x2)1/2+ a2/2 sin-1 x/a)=(a2+x2)1/2 - Maths - Continuity and Differentiability

Question

prove that d/dx( x/2 (a2
-x2)1/2+ a2/2 sin-1
x/a)=(a2+x2)1/2

Vipin Verma · Accepted Answer

ddxx2(a2-x2)1/2+a22sin-1xa=ddxx2(a2-x2)1/2+ddxa22sin-1xa=(a2-x2)1/2ddxx2+x2ddx(a2-x2)1/2
+a22ddxsin-1xa=(a2-x2)1/212+x212(a2-x2)1/2(-2x)+a221a11-x2a2=(a2-x2)1/212-x221(a2-x2)1/2+a221(a2-x2)1/2=a2-x2-x2+a22(a2-x2)1/2=2(a2-x2)2(a2-x2)1/2=(a2-x2)1/2
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