Question

How do I find the derivative of 2(f(x)+g(x))?

How do I find the derivative of
1/2(f(x) • g(x))

Answer 1

2(f(x)+g(x))

Use the product rule.

2[f'(x) + g'(x)] + (f(x)+g(x)) • (0)

Answer: 2(f'(x)+ g'(x))

Do the same for question 2.

Answer 2

`\bf 2[f(x)+g(x)]\implies 2f(x)+2g(x)\implies 2\cfrac{df}{dx}+2\cfrac{dg}{dx}\\\\ -------------------------------\\\\ \cfrac{1}{2}\left[ f(x)\cdot g(x) \right]\implies \cfrac{1}{2}\left[ \stackrel{product~rule}{\cfrac{df}{dx}\cdot g(x)+f(x)\cdot \cfrac{dg}{dx}} \right] \\\\\\ \cfrac{1}{2}\cdot \cfrac{df}{dx}\cdot g(x)+\cfrac{1}{2}\cdot \cfrac{dg}{dx}f(x)`