What is the derivative of the expression (10+lgx^10+e^10x)^10?

Since the given expression represents a composed function,
we'll evaluate its derivative applying chain rule.

We'll
put 10+lgx^10+e^10x = t

y =
t^10

We'll differentiate y with respect to
t:

dy/dt = d(t^10)/dt

dy/dt =
10t^9

We'll differentiate t with respect to
x:

dt/dx =
d(10+lgx^10+e^10x)/dx

dt/dx = 10/x +
10*e^10x

dy/dx = 10t^9*(10/x +
10*e^10x)

We'll substitute back
t:

dy/dx = 10*[(10+lgx^10+e^10x)^9]*(10/x +
10*e^10x)