Question

Derivadas: alguem me ajuda a derivar essas duas funcoes?

Answer 1

a)

Regra do quociente

f'= [(∛x+x)'*√x - (∛x+x)*(√x)']/(√x)²

f'= [(1/3)*x^(1/3 - 1) * √x -(∛x+x)*(1/2) * x^(1/2-1) ] /x

f'= [(1/3)*x^(-2/3) * √x -(∛x+x)*(1/2) * x^(-1/2) ] /x

f'= [(1/3)*x^(-1/6)  -(∛x+x)/(1/2√x) ] /x

b)

g(x)=(x+1)/(x ln (x))

g'= [(x+1)' * x*ln(x) - (x+1)*(xln(x))']/ (xln(x))²

g'= [1 * x*ln(x) - (x+1) *(ln(x) + x*(1/x))] / (xln(x))²

g' = [x*ln(x) - (x+1) *(ln(x) +1) ]/ (xln(x))²