Question

suppose f'(8)=9 and g'(8)=6

find h'(8) where h(x)=5f(x)+4g(x)+3

How do I solve this? I thought I just replaced f(x) with 9 and g(x) with 6.

Answer 1

figured it out

f'(x) = d/dx[5f(x)]+d/dx[4g(x)]+ d/dx[3]

f'(x) = 5d/dx[f(x)] + 4d/dx[g(x)]+d/dx[3]

=5 f'(x) + 4 g'(x) + d/dx [3]

h'(x) = 5 f'(x) + 4 g'(x)

h'(8) = 5(9) + 4(6)= 69