Show that, `(d)/(dx) [(x)/(2) sqrt(a^(2)-x^(2)) +(a^(2))/(2) "sin"^(-1) (x)/(a)]=sqrt(a^(2)-x^(2))`

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

The value of (d)/(dx) [ tan^(-1){(sqrt(x) (3-x))/(1-3x)}] is -

int_(0)^(1)(d)/(dx)["sin"^(-1)(2x)/(1+x^(2))]dx is equal to -

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

(d)/(dx)[sin^(2)cot^(-1)( sqrt((1-x)/(1+x)))] is equal to -

Using the formula (d)/(dx)(tan^(-1)x)=(1)/(1+x^(2)) , deduce that (d)/(dx)(cot^(-1)x)=-(1)/(1+x^(2)) .

If (d)/(dx) (2x^(3)-5)^(10)=(2x^(3)-5)^(9)f(x) , then f(x) is -

Find the value of (d)/(dx)(x(e^(x)+e^(4x))/(e^(x)+e^(-2x))) .

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)) , show that, (1-x^(2))^(2)(D^(2)y)/(dx^(2))-3x(1-x^(2)))(dy)/(dx)=1

Differentiate tan^(-1)(x/sqrt(1-x^2)) with respect to sin^(-1)((2x)*sqrt(1-x^2)),