# 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.

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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**

Given h(0) =3 and h'(0) =2 and f(x) = x*h(x).

To find f'(0).

Solution:

f(x) = xh(x).

We diffrentiate:

f'(x) = {x*h(x)}'

f'(x) = (x)'*h(x)+xh'(x)

f'(x) = h(x) +xh'(x).

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

f'(0) = 3 + 0

f'(0) = 3.

f'(x) = x)'