求函数的导数： f(x)=e^(兀x)sin(兀x)，求f`(x)及f`(1/2)

Question

“兀”为圆周率“派”

Answer 1

f'(x)=e^(兀x)*兀*sin(兀x)+e^(兀x)*cos(兀x)*兀
=兀e^(兀x)(sin兀x+cos兀x)

f'(1/2)=兀e^(兀/2)(sin兀/2+cos兀/2)
=兀e^(兀/2)

Answer 2

f(x)=e^(兀x)sin(兀x)
f'(x)=e^(兀x)sin(兀x)*兀+e^(兀x)sin(兀x)*cos(兀x)*兀x
=兀e^(兀x)sin(兀x)*[1+cos(兀x)]

f'(1/2)=兀e^(兀/2)sin(兀/2)*[1+cos(兀/2)]
=兀e^(兀/2)

Answer 3

解
f[x]=e^[πx]sinπx
f'[x]=e^[πx]'sinπx+e^[πx]sinπx'
=πxe^[πx]xsinπx+xe^[πx]cosπx
=πx^2e^[πx]sinπx+xe^[πx]cosπx

f'[1/2]=πe^[π/2]

希望对你有帮助
不懂追问