Trig Derivative - # 4

[Jason76]

\(\displaystyle y = 3xe^{x}\csc x\)

\(\displaystyle y' = [\csc x][(e^{x})(3) + (3x)(e^{x})] + [3xe^{x}][-\csc x \cot x]\)

\(\displaystyle y' = [\csc x][3e^{x} + 3xe^{x}] + [3xe^{x}][-\csc x \cot x]\)

\(\displaystyle y' = [\csc x][3e^{x}(1 + x)] + [3xe^{x}][-\csc x \cot x]\)

 

[stapel]

\(\displaystyle y = 3xe^{x}\csc x\)

\(\displaystyle y' = [\csc x][(e^{x})(3) + (3x)(e^{x})] + [3xe^{x}][-\csc x \cot x]\)

\(\displaystyle y' = [\csc x][3e^{x} + 3xe^{x}] + [3xe^{x}][-\csc x \cot x]\)

Once you multiply everything out, what terms can you combine?

\(\displaystyle y' = [\csc x][3e^{x}(1 + x)] + [3xe^{x}][-\csc x \cot x]\)

What, precisely, is your question regarding this exercise?