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) = ???
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