Question

The derivative of the function h(x) f (x)g(x)
is given in the form h′(x)  f′(x)g(x) f (x)g′(x).
Determine f (x) and g(x) for this.
h′(x) =(10x)(21 -3x) + (5x^2+7)(-3)

Answer 1

Im not sure what this question is asking for

Answer 2

Did you mean like h(x) = f(x)g(x)? If that's the case, note that both f(x) and g(x) are present in the derivative. In special, note that 10x should be f'(x) so (21 - 3x) is g(x). Can you understand it now? Sorry if my explanation was a bit unclear.

Answer 3

Im just not sure what the question is asking me to do ?

Answer 4

Typo: In particular instead of In special.

The question is asking you to find both f(x) and g(x) given the derivative of h which is a function of f and g.

It's basically like this, you have a function h(x) which is defined to be a function f(x) times another function of g(x). Then, you will apply the product rule to find its derivative, which is of the form h'(x) = f'(x)g(x) + f(x)g'(x). Note that both f and g are present in the derivate of h. Therefore, when h'(x) is defined (on the last line), you know that the first term has to be f'(x) * g(x) and so on. If the first term is f'(x) g(x), which one is g(x)? It has to be the second one, because it's f'(x) g(x).

Be careful to not overthink the problem.