Suppose that f(2) = −4, g(2) = 2, f '(2) = −1, and g'(2) = 5. Find h'(2)

Question

(a)    h(x) = 4f(x) − 3g(x)

h'(2) =  

(b)    h(x) = f(x)g(x)

h'(2) =  

(c)    h(x) = f(x)

g(x)

h'(2) = 

(d)    h(x) = g(x)

1 + f(x)

h'(2) =

Answer 1

a) h'(2) = 4f '(2) - 3g'(2) [you can plug in the associated numbers]

b) h'(2) = f '(2)g(2) + f(2)g'(2)

c) I'm assuming this problem say h(x) = f(x)/g(x). If so, h'(2) = ( f '(2)g(2) - f(2)g'(2))/(g(2))²

d) Again, I'm assuming this problem say h(x) = g(x)/(1+f(x)). If so, h'(2) = ( g'(2)(1+f(2)) - g(2)f '(2))/(1+f(2))²