Math Challenges

Solution:
\( \displaylines{f\left(t\right)=t^{\frac12}\\ f^{\prime}\left(t\right)=\frac12t^{-\frac12}=\frac{1}{2\sqrt{t}}\\ \\ g\left(s\right)=6s^{-2}\\ g^{\prime}\left(s\right)=-12s^{-3}=-\frac{12}{s^3}\\ \\ h\left(x\right)=\left(x^2-4x\right)\left(3x+15\right)\\ h^{\prime}\left(x\right)=\left\lbrack2x-4\right\rbrack\left(3x+15\right)+\left(x^2-4x\right)\left\lbrack3\right\rbrack} \)