Question

I am asked to differentiate the function y=\[\cot^{2}(\sin (x))\]. Can anyone provide a step by step tutorial? I am having difficulties with applying the chain rule. If possible avoid using Liebniz notation. Thank you!

Answer 1

\[f(x)=x^2\]\[g(x)=\cot x\]\[h(x)=\sin x\]\[D_x(f\circ g\circ h)(x)=(f'\circ g\circ h)(x)\cdot(g'\circ h)(x)\cdot h'(x)\]\[=2\cot(\sin(x))\cdot(-\csc^2(\sin x))\cdot\cos x\]

Answer 2

any particular part of that giving you trouble?

Answer 3

where did you get \[-\csc ^{2}x \sin x\] from

Answer 4

ok i got it now

Answer 5

no thank you very much. i've spent way too much time trying to figure this out!