Question

f(x)=csc^2(sqrt(t))
differentiate the above equation

Answer 1

chain rules thrice
the derivative of something cubed is 3 something squared, times the derivative of something
the derivative of cosecant of something is minus cosecant cotangent of something, times the derivative of something
the derivative of square root of something is one over two root something

Answer 2

except now that i look more carefully it is something squared
whose derivative is two something

Answer 3

in other words start with the square, write
\[2(\text{fill in the input here})\times \frac{d}{dx}\text{rest of input}\]
then
\[2(\text{fill in the input here})\times -\csc(\text{input})\cot(\text{input})\times \frac{1}{2\sqrt{x}}\]