Question

No clue how to solve can somoene please explain.

Let f and g be differentiable functions with following properties
1)g(x)>0 for all x
2)f(0)=1

If h(x)=F(x)g(x) and h'(x)=f(x)g'(x), then f(x)=

a)f'(x) b)g(x) c)e^x d)0 e)1

Answer 1

if h(x)=f(x)g(x) then generally h'(x)=f'(x)g(x)+f(x)g'(x), so in this case i think the answer would be e: f(x)=1

Answer 2

ooh so you use product rule?

Answer 3

right, e^x looks close but its not the product rule if f(x)=e^x then with h(x)=e^xg(x) then h'(x)=e^xg(x) + e^xg'(x)

Answer 4

if f(x) = 1 then h'(x) = 1* g'(x)+0g(x)

Answer 5

ah get it now
thanks soo much

Answer 6

yup

Answer 7

Nice!