use logarithmic differentiation to find the derivative of the function y = (sqrt x)e^((x^2) - x) (x + 1)^(2/3)
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You need to take logarithms both sides such that:
`ln y = ln((sqrt x)e^((x^2) - x)(x + 1)^(2/3))`
Using logarithmic identities yields:
`ln y = ln sqrt x + ln e^(x^2 - x) + ln (x+1)^(2/3)`
`ln y = (1/2)ln x + (x^2 - x) ln e + (2/3) ln (x+1)`
Since `ln e = 1` yields:
`ln y = (1/2)ln x + (x^2 - x) + (2/3) ln (x+1)`
Differentiating both sides with respect to x yields:
`(1/y)*y' = 1/(2x) + 2x - 1 + 2/(3(x+1))`
`y' = y(1/(2x) + 2x - 1 + 2/(3(x+1))) `
Substituting `((sqrt x)e^((x^2) - x)(x + 1)^(2/3))` for y yields:
`y' = ((sqrt x)e^((x^2) - x)(x + 1)^(2/3))*(1/(2x) + 2x - 1 + 2/(3(x+1))) `
Hence, diferentiating the given function using logarithmic differentiation yields `y' = ((sqrt x)e^((x^2) - x)(x + 1)^(2/3))*(1/(2x) + 2x - 1 + 2/(3(x+1))).`
Related Questions
- `y = sqrt((x-1)/(x^4 + 1))` Use logarithmic differentiation to find the derivative of the...
- 1 Educator Answer
- `y = sqrt(x) e^(x^2 - x) (x + 1)^(2/3)` Use logarithmic differentiation to find the...
- 3 Educator Answers
- `y = sqrt(x + sqrt(x + sqrt(x)))` Find the derivative of the function.
- 2 Educator Answers
- `G(y) = ln(((2y+1)^5)/(sqrt(y^2 + 1)))` Differentiate the function.
- 1 Educator Answer
- logarithmic differentiation to find the derivative of the equationy=(sqrt(x))^(5x)
- 1 Educator Answer