Find the derivative of the given function. g ( x ) = 7 e x + 2 x 3 g(x)=7e^x+2x^3 g ( x ) = 7 e x + 2 x 3

Here, we wanna find the derivative of the function g of x equals 7e to the x plus 2x cubed. So to find this derivative here, g prime of x, since I have 2 functions being added together, I can just add their derivatives in order to get the derivative of this entire function. So taking a look at that first term, 7 e to the x, we know that the derivative of e to the x is just e to the x. And from our constant multiple rule, we know that having a constant there is just going to leave our constant in that derivative. So this is 7 times the derivative of e to the x, which is just e to the x. Then adding this together with the derivative of 2x cubed, we can apply the power rule here, pulling that 3 out front, multiplying by it, then decreasing that power by 1. This gives us 6x squared. So my derivative here, g prime of x, is 7e to the x plus 6x squared. I'll see you in the next one.