Question

函数y=（x^2-x+1)^x的导数

Answer 1

函数y=（x²-x+1)^x的导数

两边取对数：lny=xln(x²-x+1)

两边对x取导数：y′/y=ln(x²-x+1)+x(2x-1)/(x²-x+1)

故y′=y[ln(x²-x+1)+(2x²-x)/(x²-x+1)]=[(x²-x+1)^x][ln(x²-x+1)+(2x²-x)/(x²-x+1)]