Find `(dy)/(dx)` for `y=((x^2+2)(x+sqrt2))/(sqrt(x+4)(x-7))`

Find (dy)/(dx) for y =(x^2 + 4x + 6)^5

Find (dy)/(dx) for y=log(x+sqrt(a^2+x^2))dot

Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x)-1)/(sqrt(x)+1))

Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

Find (dy)/(dx) for the function: y=sqrt(sinsqrt(x))

If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a) (e^(sqrt(x)))/(2sqrt(x)) (b) (e^(sqrt(x))-e^(-sqrt(x)))/(2x) 1/(2sqrt(x))sqrt(y^2-4) (d) 1/(2sqrt(x))sqrt(y^2+4)

The function y=f(x) is the solution of the differential equation (dy)/(dx)+(x y)/(x^2-1)=(x^4+2x)/(sqrt(1-x^2)) in (-1,1) satisfying f(0)=0. Then int_((sqrt(3))/2)^((sqrt(3))/2)f(x)dx is

(a) Find (dy)/(dx) where y=(x^(2)+1)root(3)(x^(2)+2) (b) Evaluate int (x+1)sqrt(2x+3) .

Find (dy)/(dx)," if "x= at^(2), y= 2at .

(x+a)(dy)/(dx)-2y=(x+a)^(4)