There is an ambiguity with what you wrote, but I assume the function is
#y = (xsqrt(2x+1))/(e^x sin^3(x)) #
We can use quotient rule:
#d/dx(f/g) = (gf' - fg')/g^2 #
Using this definition:
#f(x) = xsqrt(2x+1) implies f'(x) = sqrt(2x+1) + (x)/sqrt(2x+1) = (3x+1)/sqrt(2x+1)#
#g(x) = e^x sin^3x implies g'(x) = e^x sin^3(x) + 3e^xsin^2(x)cos(x)#
#dy/dx = ((e^x sin^3x (3x+1))/sqrt(2x+1) - xsqrt(2x+1) * (e^x sin^3(x) + 3e^xsin^2(x)cos(x)) ) / (e^x sin^3x)^2#
#dy/dx = (3x+1)/(e^xsin^3xsqrt(2x+1)) - (xsqrt(2x+1) * (sinx + 3cosx) ) / (e^x sin^4x) #
