Question
how would you find the derivative of:
f(x) = (x^2 + 1)^ (2-3x)
f(x) = (x^2 + 1)^ (2-3x)
Answers
Reiny
Let y = (x^2 + 1)^ (2-3x)
take ln of both sides
lny = (2-3x)ln(x^2 + 1)
(dy/dx)/y = (2-3x)(2x)/(x^2 + 1) - 3ln(x^2 + 1)
dy/dx = y((2-3x)(2x)/(x^2 + 1) - 3ln(x^2 + 1))
you could replace y with the original if you want to
take ln of both sides
lny = (2-3x)ln(x^2 + 1)
(dy/dx)/y = (2-3x)(2x)/(x^2 + 1) - 3ln(x^2 + 1)
dy/dx = y((2-3x)(2x)/(x^2 + 1) - 3ln(x^2 + 1))
you could replace y with the original if you want to