Post Edited
\(\displaystyle y = \cot^{4} 2x\)
\(\displaystyle y' = 4 (\cot^{3} 2x) (- \csc^{2} 2x) 2\) :-? The cotangent trig name isn't changed on the left, but changes in other places.
\(\displaystyle y' = - 8 \cot^{3} 2x \csc^{2} 2x\)
Ok, I see the logic behind this, but note this is different than:
\(\displaystyle y = \cot 2x\)
\(\displaystyle y' = -\csc^{2} 2x (2)\) The cotangent trig name is changed (to cosecent). There are no instances of it staying the same anywhere.
\(\displaystyle y' = -2 \csc^{2} 2x\)
Ok, I see how this is done (when you see a trig function to a power other than 1, you don't change the trig function name) and can replicate. But don't really understand the logic behind the trig function name changing.
\(\displaystyle y = \cot^{4} 2x\)
\(\displaystyle y' = 4 (\cot^{3} 2x) (- \csc^{2} 2x) 2\) :-? The cotangent trig name isn't changed on the left, but changes in other places.
\(\displaystyle y' = - 8 \cot^{3} 2x \csc^{2} 2x\)
Ok, I see the logic behind this, but note this is different than:
\(\displaystyle y = \cot 2x\)
\(\displaystyle y' = -\csc^{2} 2x (2)\) The cotangent trig name is changed (to cosecent). There are no instances of it staying the same anywhere.
\(\displaystyle y' = -2 \csc^{2} 2x\)
Ok, I see how this is done (when you see a trig function to a power other than 1, you don't change the trig function name) and can replicate. But don't really understand the logic behind the trig function name changing.
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