Calculus 10th Edition

$g'(t)=\frac{1}{4\sqrt[4]{t^3}}-6\csc(t)\cot(t)$
$g(t)=f(t)+h(t)\rightarrow f(t)=\sqrt[4]{t}$ ; $h(t)=6\csc(t)$ Using the Power Rule: $f'(t)=\frac{1}{4}t^{\frac{1}{4}-1}=\frac{1}{4\sqrt[4]{t^3}}$ By Theorem 2.9 and Constant Multiple Rule: $h'(t)=6(\dfrac{d}{dt}\csc(t))$ $=6(-\csc(t)\cot(t))$ $=-6\csc(t)\cot(t)$ Using the Sum Rule: $g'(t)=f'(t)+h'(t)=\frac{1}{4\sqrt[4]{t^3}}-6\csc(t)\cot(t)$