the derivative of $g(x)=e^{x}(13x^{2}-26x + 20)$ is $\\square$
the derivative of $g(x)=e^{x}(13x^{2}-26x + 20)$ is $\\square$
Answer
Explanation:
Step1: Apply product - rule
The product - rule states that if (y = u\cdot v), then (y^\prime=u^\prime v + uv^\prime). Let (u = e^{x}) and (v = 13x^{2}-26x + 20). The derivative of (u = e^{x}) is (u^\prime=e^{x}), and the derivative of (v = 13x^{2}-26x + 20) is (v^\prime=26x-26).
Step2: Calculate (g^\prime(x))
[ \begin{align*} g^\prime(x)&=u^\prime v+uv^\prime\ &=e^{x}(13x^{2}-26x + 20)+e^{x}(26x - 26)\ &=e^{x}(13x^{2}-26x + 20+26x - 26)\ &=e^{x}(13x^{2}-6) \end{align*} ]
Answer:
(e^{x}(13x^{2}-6))