Question

Let f and g be functions that satisfy f′(2)=−2 and g′(2)=11. Find h′(2) for each function h given below:

(A) h(x)=6f(x).

h′(2) =


(B) h(x)=−5g(x).
h′(2) =


(C) h(x)=10f(x)+9g(x).

h′(2) =


(D) h(x)=8g(x)−11f(x).

h′(2) =


(E) h(x)=2f(x)+11g(x)−12.

h′(2) =


(F) h(x)=−2g(x)−3f(x)+10x.

h′(2) =

Answer 1

@Michele_Laino

Answer 2

hint:
case a)
\[h'\left( x \right) = 6f'\left( x \right)\]

case b)
\[h'\left( x \right) = - 5g'\left( x \right)\]

case c)
\[h'\left( x \right) = 10f'\left( x \right) + 9g'\left( x \right)\]

case d)
\[h'\left( x \right) = - 11f'\left( x \right) + 8g'\left( x \right)\]

case e)
\[h'\left( x \right) = 2f'\left( x \right) + 11g'\left( x \right)\]

case f)
\[h'\left( x \right) = - 3f'\left( x \right) - 2g'\left( x \right) + 10\]