find derivative of f(t) = t(16-t^2)

Question

Please explain how the derivative of f(t) = t(16 - t^2)

Answer 1

We know that d/dx(x) = 1

d/dx(x^n) = nx^n-1

Given f(t) = t(16-t^2)

= 16t-t^3

Apply derivative with respect of t.

d/dt(f(t)) = d/dt(16t-t^3)

= d/dt(16t)-d/dt(t^3)

= 16-3t^2