Question

derive com ln a função
y=x^ln​

Answer 1

Resposta:

Se for y=x^(ln(x))

ln(y) =ln (x)^(ln(x))

ln(y) =ln(x) *ln(x)

y=e^[ln(x) *ln(x)]

y'=[ln(x) *ln(x)]' * e^[ln(x) *ln(x)]

y=e^[ln(x) *ln(x)]

y'=[ln(x) *ln(x)]' * y

y'=[ln(x) *ln(x)]' * x^(ln(x))

y'=[(1/x) * ln(x) +ln(x) * (1/x)] * x^(ln(x))

y'=[(2/x) * ln(x)] * x^(ln(x))

y'=[(2ln(x)/x] * x^(ln(x))

y'=(ln(x²)*(1/x)* x^(ln(x))

y'=(ln(x²) * x^(ln(x)-1)