Question

Just plug in the numbers then find the derivative.

h(x)=f(g(x))
f(x)=sqrt(x)
g(x)=5x^2+4
h(3)=[]
h'(3)=[]/[]

Answer 1

h(3) = 7

h'(3) = 15/7

Explanation:

h(3) = f(g(3)) = f(5(3²)+4)

h(3) = f(49)

h(3) = 7

h(x) = (5x² + 4)^½

h'(x) = ½[(5x² + 4)^-½] × 10x

h'(x) = 5x[(5x² + 4)^-½]

h'(3) = 5(3)/7 = 15/7