Question

To find the second derivative of a function, you typically follow these steps:

1. Start with the first derivative of the function.
2. Differentiate the first derivative with respect to the variable of interest.
In your provided question, it seems like you want to find the second derivative of a function denoted as g(x). You've also provided the first derivative as:
g′(x)=31(x3+6x2+9x)−32(3x2+12x+9)

Answer 1

To find the second derivative of a function, you start with the first derivative and differentiate it with respect to the variable of interest. For the given function g(x), the second derivative is 93x^2 + 180x - 1065.

Step-by-step explanation:

To find the second derivative of a function, you typically follow these steps:

Start with the first derivative of the function.

Differentiate the first derivative with respect to the variable of interest.

In the provided question, you want to find the second derivative of a function denoted as g(x). The first derivative is given as:

g'(x) = 31(x^3 + 6x^2 + 9x) - 32(3x^2 + 12x + 9)

To find the second derivative, we need to differentiate g'(x) with respect to x. Let's do that:

g''(x) = d/dx(g'(x))

Using the power rule and linearity of differentiation, we can differentiate each term in g'(x) separately:

g''(x) = d/dx(31(x^3 + 6x^2 + 9x)) - d/dx(32(3x^2 + 12x + 9))

g''(x) = 93x^2 + 372x + 279 - 192x - 768 - 576

g''(x) = 93x^2 + 180x - 1065