find and simplify the derivative of the following function. g(x)=e^x(13x^2 - 26x + 26) which of the…

find and simplify the derivative of the following function. g(x)=e^x(13x^2 - 26x + 26) which of the following shows how to find the derivative of g(x)? a. g(x)=(e^x)(d/dx(e^x))+(13x^2 - 26x + 26)(d/dx(13x^2 - 26x + 26)) b. g(x)=(13x^2 - 26x + 26)(d/dx(13x^2 - 26x + 26))+(e^x)(d/dx(e^x)) c. g(x)=d/dx(e^x)(13x^2 - 26x + 26)+(e^x)d/dx(13x^2 - 26x + 26) d. g(x)=(13x^2 - 26x + 26)(d/dx(e^x))+(e^x)(d/dx(13x^2 - 26x + 26))

find and simplify the derivative of the following function. g(x)=e^x(13x^2 - 26x + 26) which of the following shows how to find the derivative of g(x)? a. g(x)=(e^x)(d/dx(e^x))+(13x^2 - 26x + 26)(d/dx(13x^2 - 26x + 26)) b. g(x)=(13x^2 - 26x + 26)(d/dx(13x^2 - 26x + 26))+(e^x)(d/dx(e^x)) c. g(x)=d/dx(e^x)(13x^2 - 26x + 26)+(e^x)d/dx(13x^2 - 26x + 26) d. g(x)=(13x^2 - 26x + 26)(d/dx(e^x))+(e^x)(d/dx(13x^2 - 26x + 26))

Answer

Explanation:

Step1: Recall the product - rule

The product - rule states that if (y = u\cdot v), where (u) and (v) are functions of (x), then (y^\prime=u^\prime v + uv^\prime). Here, (u = e^{x}) and (v=13x^{2}-26x + 26).

Step2: Find the derivatives of (u) and (v)

The derivative of (u = e^{x}) with respect to (x) is (\frac{d}{dx}(e^{x})=e^{x}), and the derivative of (v = 13x^{2}-26x + 26) with respect to (x) is (\frac{d}{dx}(13x^{2}-26x + 26)=26x-26).

Step3: Apply the product - rule

(g^\prime(x)=\frac{d}{dx}(e^{x})(13x^{2}-26x + 26)+e^{x}\frac{d}{dx}(13x^{2}-26x + 26))

Answer:

A. (g^\prime(x)=(e^{x})\left(\frac{d}{dx}(e^{x})\right)+(13x^{2}-26x + 26)\left(\frac{d}{dx}(13x^{2}-26x + 26)\right))