Question

qual a derivada de: cotg(x-2/x²+4)

Answer 1

v = (x-2)/(x²+4)
v ' = [1.(x²+4) - 2x(x-2)]/(x²+4)²
v ' = [x²-4 -2x²+2x]/(x²+4)²
v ' = [-x²+2x -4]/(x²+4)²
v ' = -[x²-2x +4]/(x²+4)²

z = cotgv
z ' = -cossec²v
A derivada de y = cotg(x-2/x²+4) é:

y ' = v ' * k'

y ' =-[x²-2x +4]/(x²+4)²-cossec²v

y ' = -[x²-2x +4]/(x²+4)²*{-cossec²[(x-2)/(x²+4)]}
y ' = [x²-2x +4]/(x²+4)²cossec²[(x-2)/(x²+4)]