How do you find the derivative of f(t)=(4-t)^3?

2 Answers
Mar 7, 2018

f(t)=(-3)(4-t)^2

Explanation:

d/dt=3*(4-t)^2*d/dx(4-x)
=3*(4-t^2)*-1
=(-3)(4-t)^2

Mar 7, 2018

-3(4-t)^2

Explanation:

According to the chain rule, (df)/dx=(df)/(du)*(du)/dx, where u is a function within f.

Here, f=u^3 where u=4-t, so we have:

d/(du)u^3*d/dx(4-x)

3u^2*-1

-3u^2, but since u=4-t, we have:

-3(4-t)^2