Let `y=((3^x-1)/(3^x+1))sinx+log_e(1+x), x gt 1` then at x=0 , `dy/dx=`

Let y=((3^x-1)/(3^x+1))sinx+log_e(2+x),xgt-1 . Then at x=0 dy/dx equals

If 3f(x)-f((1)/(x))= log_(e) x^(4) for x gt 0 ,then f(e^(x))=

1.If y = (log x)3 then dy/dx=

If y=log(1/x) , show that dy/dx+e^y=0

x (dy)/(dx) - y = ( x-1 ) e ^(x), x gt 0

If y=5^(2{log_(5)(x+1)-log_(5)(3x+1)}) then (dy)/(dx) at x=0 is

If y=1+(1)/(x)+(1)/(x^(2))+(1)/(x^(3))+… to oo with |x|gt 1 then (dy)/(dx)=

Let y(x) be the solution of the differential equation ( x log x) (dy)/(dx) + y = 2x log x, ( x gt 1). then y (e) is equal to :