Question

设y=(1+sinx)^x,则dy|x=π

Answer 1

y=(1+sinx)^x

lny=ln(1+sinx)^x=xln(1+sinx)

y'/y=ln(1+sinx)+xcosx/(1+sinx)

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

dy/dx|x=π =-π