Question

perguntas logo abaixo, pfv alguém ajuda ai, matemática aplicada!

Answer 1

a) f(x)=2x²-x-1

f'(x)=4x-1

b) f(x)=2√x -x²+1/x²

f(x)=2*x^(1/2) -x²+x^(-2)

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

f'(x)=1/√x -2x-2/x³

c) g(x)=(x²-2x)*(4x³+5x)

g'(x)=(x²-2x)'*(4x³+5x)+(x²-2x)*(4x³+5x)'

g'(x)=(2x-2)*(4x³+5x)+(x²-2x)*(12x²+5)

d) h(x)=(1-x)/(x+3)

h'(x)=[(1-x)'*(x+3) -(1-x)*(x+3)']/(x+3)²

h'(x)=[(-1)*(x+3) -(1-x)*(1)]/(x+3)²

h'(x)=[-(x+3) -(1-x)]/(x+3)²

h'(x)=-4/(x+3)²

e) g(x)=1/√(2x-5)

g(x)=(2x-5)^(-1/2)

g'(x)=(-1/2)*(2x-5)^(-1/2-1)

g'(x)=(-1/2)*(2x-5)^(-3/2)

g'(x)=-1/(2*(2x-5)^(3/2))

g'(x)=-1/(2*√(2x-5)³)