#1 Find y' of y=9^(-x)

My work:

y' = 9^(-x) * ln(9) * (-x)'

y' = -9^(-x) * ln(9)

#2 Find y' of y = ln((3-x)/(3+x))

y' = 1/((3-x)/(3+x)) * ((3-x)/(3+x))'

y' = 1/((3-x)/(3+x)) * ((3-x)'(3+x)-(3-x)(3+x)')/(3+x)^2

y' = (3+x)/(3-x)* ((-1)(3+x)-(3-x)(1))/(3+x)^2

y' = (3+x)/(3-x)* (-3-x-3+x)/(3+x)^2

y' = 1/(3-x) * -6/(3+x)

y' = -6/((x+3)(x-3)

y' = -6/(x^2-9)

#3 Find y' of y = ln((x(x^2+2)/(sqrt(x^3-7))

Answers from my teacher:

#1 (-2)(3^(-2x)(ln(3))

#2 6/(x^2-9)

#3 (1/x) + (2x)/(x^2+2) - (3x^2)/(2(x^3-7))