Question

Find f′ in terms of g′

f(x)=x2g(x)

Select one:

f′(x)=2xf′(x)+2xg′(x)


f′(x)=2xg′(x)


f′(x)=2x+g′(x)


f′(x)=x2g(x)+2x2g′(x)


f′(x)=2xg(x)+x2g′(x)

Answer 1

9514 1404 393

Answer:

(e) f′(x)=2xg(x)+x²g′(x)

Explanation:

The product rule applies.

(uv)' = u'v +uv'

__

Here, we have u=x² and v=g(x). Then u'=2x and v'=g'(x).

f(x) = x²·g(x)

f'(x) = 2x·g(x) +x²·g'(x)