In the given problem f(x)=x*h(x), find f`(0) given that h(0)=3 and h`(0)=2, where f`and h`mean f prime and h prime.

Here we are given with the relation f(x) =
x*h(x)

Now we have to differentiate f(x) to get the
required answer. Using the product rule which states that the derivative of f(x)*g(x) is
f'(x)*g(x) + f(x)*g'(x) we get :

f(x) =
x*h(x)

=> f'(x) = x*h'(x) +
h(x)*1

Now for x =0 ,

f'(0) =
0* h'(0) + h(0)

=> 0 +
3

=> 3.

Here we don't
need to use h'(0) = 2 as it is being multiplied with 0 and therefore gets
eliminated.

So the required value for f'(0)
is 3