Use logarithmic differentiation to find the derivative of the function y=\sqrt{x}e^x^4(x^2+1)^7. y'=?

Answer 1

I'm guessing that the original equations is

y = √x•e^{x^4}•(x²+1)⁷

ln(y) = ln(x)/2 + x⁴ln(e)+ 7ln(x²+1) --> note ln(e) = 1 or ln(e^z) = z

Taking the derivative of both sides

y '/y = 1/(2x) + 4x³ + 7(2x)/(x²+1)

y ' = y(1/(2x) + 4x³ + 7(2x)/(x²+1)) = (√xe^{x^4}(x²+1)⁷)(1/(2x) + 4x³ + 7(2x)/(x²+1))

Which could be simplified