The derivative of `y=2^(x^3+2x)`

We will use the following rules and formulas:

• Chain rule `(f(g(x)))'=f'(g(x))cdot g'(x)`
  


• Derivation of exponential function `(a^x)'=a^x ln a`
  


• Derivation of sum `(f(x)+g(x))'=f'(x)+g'(x)` 


• Derivation of power `(x^n)'=nx^(n-1)`
  

First we apply chain rule and derivation of exponential function.

`y'=2^(x^3+2x)ln2cdot(x^3+2x)'`

Now we apply derivation of sum.

`=2^(x^3+2x)ln2cdot((x^3)'+(2x)')`

Now we apply derivation of power.

`=2^(x^3+2x)ln2cdot(3x^2+2)`

Therefore, the solution is `y'=2^(x^3+2x)ln2cdot(3x^2+2)`