Find the derivative of the function fz fz t63t9t5 fz Soluti

Find the derivative of the function f(z)

f(z)= (t^6+3t+9)/(t+5)

f\'(z) = ???

Solution

f(z)=f(x)/g(x) where f(x)=t^6+3t+9 g(x)=t+5 f\'(z)=(f\'(x)g(x)-f(x)g\'(x))/g(x)^2 f\'(x)=6t^5+3 g\'(x)=1 f\'(z)=((6t^5+3)(t+5)-(t^6+3t+9))/(t+5)^2 =6t^6+6t^5+3t+15-t^6-3t-9/(t+5)^2 =(5t^6+6t^5+6)/(t+5)^2
Find the derivative of the function f(z) f(z)= (t^6+3t+9)/(t+5) f\'(z) = ???Solution f(z)=f(x)/g(x) where f(x)=t^6+3t+9 g(x)=t+5 f\'(z)=(f\'(x)g(x)-f(x)g\'(x))/

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