यदि `(1)/(2) (e^(y) - e^(-y)) = x` हो, तो सिध्द कीजिए कि `(dy)/(dx) = (1)/(sqrt(1+x^(2)))`

Find (dy)/(dx) of y=e^((x^(2))/(1+x^(2)))

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

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

If x^(y) = e^(x - y) prove that (dy)/(dx) = (log_(e)x)/((1 + log_(e)x)^(2)) .

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

find the order and degree of D.E : (1) ((d^(2)y)/(dx^(2) ))^2 + ((dy)/(dx))^(3) = e^(x) (2) sqrt(1 + 1/((dy)/(dx))^(2))= ((d^(2)y)/(dx^(2)))^(3/2) (3) e^((dy)/(dx))+ (dy)/(dx) =x

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

If y = e^(log_(e) [1 + x + x^(2) + …]) , then (dy)/(dx) =