How do you differentiate f(x)=e^sqrt(3lnx+x^2) using the chain rule.?

1 Answer
Jan 16, 2016

dy/dx=(e^sqrt(3lnx+x^2) * (3/x+2x))/((2sqrt(3lnx+x^2))

Explanation:

The chain rule:

dy/dx=dy/(du) * (du)/(dv)*(dv)/(dx)

y = e^u, dy/(du)=e^u

u=v^(1/2), (du)/(dv)=1/2v^-(1/2)

v=3lnx+x^2, (dv)/dx=3/x+2x

dy/dx=e^u*1/(2sqrtv)*(3/x+2x)

dy/dx=(e^sqrt(3lnx+x^2) * (3/x+2x))/((2sqrt(3lnx+x^2))