18y((1)/(sqrt(1-e^(2x)))

If y=sqrt((1+e^x)/(1-e^x)),s howt h a t(dy)/(dx)=(e^x)/((1-e^x)sqrt(1-e^(2x)))

If y=sqrt((1+e^(x))/(1-e^(x))) , show that (dy)/(dx)=e^(x)/((1-e^(x))sqrt(1-e^(2x))) .

Solve the following differential equations. (i) (dy)/(dx) =(1+y^(2))/(1+x^(2)) (ii) (dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2))) (iii) (dy)/(dx) = 2y tan hx (iv) sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0 (v) (dy)/(dy) = e^(x-y)+x^(2)e^(-y)

If y = sqrt((1+e^x)/(1-e^x)), show that dy/dx = e^x/((1-e^x) sqrt(1-e^2x)), x < 0

If y=sqrt((1+e^(x))/(1-e^(x))), show that (dy)/(dx)=(e^(x))/((1-e^(x))sqrt(1-e^(2)x))

int_(-1)^((1)/(2))(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2))) is equal to (sqrt(e))/(2)(sqrt(3)+1) (b) (sqrt(3e))/(2)sqrt(3e)(d)sqrt((e)/(3))

int_(-1)^(1//2)(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2))) is equal to a) (sqrt(e))/(2)(sqrt(3)+1) b) (sqrt(3e))/(2) c) sqrt(3e) d) sqrt(e/3)

if y=log(e^(2x)+sqrt(1+e^(4x))) and y_(1)sqrt(1+e^(4x))=me^(mx) then m=

intsqrt((e^x+1)/(e^x-1))dx (A) ln (e^(x)+sqrt(e^(2x)-1))-sec^(-1)(e^(x)) +C (B) ln(e^(x)+sqrt(e^(2x)-1))+sec^(-1)(e^(x))+C (C) ln (e^(x)-sqrt(e^(2x)-1))-sec^(-1)(e^(x)) +C (D) ln(e^(x)+sqrt(e^(2x)-1))-sin^(-1)(e^(-x))+C