Question

Can someone explain to me how to get the derivative of
f(x)=t sqrt(4-t^2)

Answer 1

You need a Product Rule and a Chain Rule. Let's see what you get.

Answer 2

write the sqrt term as (4 - t^2)^ 0.5

can you differentiate this? use the Chain rule

Answer 3

\(\bf\large \sqrt{4-t^2}\implies t^1\cdot {\color{blue}{ (4-t^2)^{\frac{1}{2}}}}\)

as already pointed out, product rule, and you'd chain rule the binomial

Answer 4

ahemm rather -> \(\bf \large f(t)=t\sqrt{4-t^2}\implies t^1\cdot {\color{blue}{ (4-t^2)^{\frac{1}{2}}}}\)