How do you find the derivative of the function #g(t)=(4t)/(t+1)#?

1 Answer
mason m
Nov 9, 2016

#g'(t)=4/(t+1)^2#

Explanation:

Use the quotient rule. The quotient rule states that the quotient of two functions, such as some function #y=u/v#, where #u# and #v# are functions of #x#, has a derivative of #dy/dx=((du)/dx*v-u*(dv)/dx)/v^2#.

So, applying this to the function at hand, we see that:

#g(t)=(4t)/(t+1)#

#g'(t)=((d/dt4t)*(t+1)-4t(d/dt(t+1)))/(t+1)^2#

#color(white)(g'(t))=(4(t+1)-4t(1))/(t+1)^2#

#color(white)(g'(t))=4/(t+1)^2#

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