Question

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

Answer 1

`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`