If g'(5)=10 and h'(5)= -4, find f''(5) for f(x)=3g(x)-2h(x)+3?

Question

anonymous · Answer

$$\frac{ df }{ dx }=3*\frac{ d }{ dx }\left[ g(x) \right]-2*\frac{ d }{ dx }\left[ h \left( x \right) \right]+0$$
by the sum/difference rules, constant multiple rule, and constant rule for differentiation.
This simplifies to
$$f \prime(x)=3*g \prime(x)-2*h \prime(x)$$
In the same way,
$$f \prime \prime(x)=3*g \prime \prime(x)-2*h \prime \prime(x)$$
and
$$f \prime \prime(5)=3*g \prime \prime(5)-2*h \prime \prime(5)$$
Since no information is given on $$g \prime \prime(5)$$
and 
$$h \prime \prime(5)$$
I believe this problem cannot be solved.

However, if there is a typo, and the problem is actually asking for $$f \prime(5)$$
then
$$f \prime(5)=3*g \prime(5)-2*h \prime(5)$$
$$f \prime(5)=3*10-2*-4$$
$$f \prime(5)=38$$