How do you find the derivative of s=1/3t^3+1/2t^2+t?

1 Answer
Feb 10, 2017

(ds)/dt=t^2+t+1

Explanation:

We will use the rules:

  • d/dt[f(t)+g(t)]=d/dtf(t)+d/dtg(t)
  • d/dtt^n=nt^(n-1)
  • d/dta*f(t)=a*d/dtf(t)

Then:

(ds)/dt=1/3(d/dtt^3)+1/2(d/dtt^2)+d/dtt^1

(ds)/dt=1/3(3t^2)+1/2(2t^1)+1t^0

(ds)/dt=t^2+t+1