Question

how would you find the derivative of:

f(x) = (x^2 + 1)^ (2-3x)

Answer 1

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