Derivative homework hep | Mathematics homework help

consider the function r(t)= t^t and s(t)=arcos(t), for which you are given the facts that r'(t)=t^t(ln(t)+1) and s'(t)=-1/square root 1-t^2.
Do not be connected with where these derivative formulas come from. we restrict our interest in both functions to the domain 0<t<1.

1) let w(t)=3t^t-2 arcos (t). Determine w’ (t).

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2) find an equation for the tangent line to y=w(t) at the point (1/2 , w(1/2)).

3) let u(t)=t^t + arcos(t). is u increasing or decreasing the the instant t=1/2? why?


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