Diffrention of functions

Question

Differentiate.

f(x) = 2xe^x csc x

Answer 1

For d(2xe^xcsc x)/dx, first take the derivative of 2xe^x equal to 2e^x+2xe^x.

Next, with the derivative of csc x being the derivative of 1/sin x, write d(csc x)/dx

equals [sin x(0) - (1)cos x]/sin²x or -cos x/sin²x or -cot x(csc x).

Finally, obtain d(2xe^xcsc x)/dx as d(2xe^x)/dx Times csc x + 2xe^x Times d(csc x)/dx

which equals (2e^x+2xe^x)csc x + 2xe^x(-cot x•csc x) or csc x(2e^x+2xe^x-2xe^xcot x)

or 2e^xcsc x(1+x-xcot x).