We have the function g(x) = 2x^3 + 5x^2 -3x + 7.

The derivative of x^n = n*x^(n - 1)

g(x) = 2x^3 + 5x^2 -3x + 7

=> g'(x) = 3*2*x^2 + 2*5*x - 3

=> g'(x) = 6x^2 + 10x - 3

**The required derivative is 6x^2 + 10x - 3**

We have the function g(x) = 2x^3 + 5x^2 - 3x + 7.

We need to find the first derivative of g(x).

By definition we know that the derivative of ax^b = a*b*x^(b-1).

Then, we will apply the rule to all terms.

==> g'(x) = (2x^3)' + (5x^2)' -(3x)' + (7) '

==> g'(x) = 6x^2 + 10x - 3 + 0

Then, the first derivative is g'(x) and given by:

**==> g'(x) = 6x^2 + 10x -3 **