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" 7"(d)/(dx){sin^(-1)x+sin^(1)sqrt(1-x^(...

" 7"(d)/(dx){sin^(-1)x+sin^(1)sqrt(1-x^(2))}

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Prove that (d)/(dx)(sin^(-1)x)=(1)/(sqrt(1-x^(2)) , where x in [-1,1].

(d)/(dx) {Sin ^(-1) ""(sqrt((1-x)/2)}=

(d)/(dx)[sin^(-1)((sqrt(1+x)+sqrt(1-x))/(2))]=

d/(dx) (sin^(-1) x/a)

(d)/(dx ) {Sin ^(-1) ""(x)/( sqrt(1+ x^(2)))}=

(d)/(dx) {Sin ^(-1) ""(2x)/(1+ x ^(2))}=

(d)/(dx)[sin^(-1)sqrt(((1-x))/(2)]=

(d)/(dx)[sin^(-1)sqrt(((1-x))/(2))]=

d/(dx)[sin^(- 1)((sqrt(1+x)+sqrt(1-x))/2)]=