Question

If f(4) = 8, g(4) = 2, f(-4) = 1, g(-4) = 3, f'(4) = 10, g'(4) = 12, f'(-4) = 6, and g'( -4) = -2, find H'(4) where H(x) = g( f(x)- 3x).

Answer 1

how do i solve this?

Answer 2

h= g (f(x)-3x)

h'(x) = ( f '(x) -3 ) g ' ( f(x) -3x) , by chain rule

Answer 3

now sub the value

h'(4) = ( f'(4) -3) g ' ( f(4) -12)

Answer 4

H'(x) = g'(f(x) - 3x) * (f'(x) - 3)
H'(4) = g'(f(4) - 3*4) * (f'(4) - 3)
= g'(8 - 12) * (10 - 3)
= g'(-4) * 7
= -2*7
= -14

Answer 5

but f(4) =8 , and f'(4) = 10

Answer 6

etc ^

Answer 7

thank you!!!!!:))

Answer 8

chain rule confuses me so much