Question

Pls help with picture #1, and #2 is the example/how to do it. Thank you :)

Answer 1

The given function is

`h(x)=(f(x))/(g(x))`

Differentiate with respect x, by using the quotient rule.

`h^(\prime)(x)=(f^(\prime)(x)g(x)-g^(\prime)(x)f(x))/((g(x))^2)`

Set x=4, we get

`h^(\prime)(4)=(f^(\prime)(4)g(4)-g^(\prime)(4)f(4))/((g(4))^2)`
`\text{Substitute }f^(\prime)(4)=5,f(4)=3,g^(\prime)(4)=7\text{ and }g(4)=9,\text{ we get}`
`h^(\prime)(x)=(5*9-7*3)/((9)^2)`

`h^(\prime)(x)=(45-21)/(81)=(24)/(81)=(8)/(27)`

Hence the required value is

`h^(\prime)(4)=(8)/(27)`