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

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

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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)

User Sidd Thota
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