y=e^sin(x^2+根号x),求dy

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/06 04:44:49
y=e^sin(x^2+根号x),求dyy=e^sin(x^2+根号x),求dyy=e^sin(x^2+根号x),求dy解y''=[e^sin(x²+√x)]''=e^sin(x²+√

y=e^sin(x^2+根号x),求dy
y=e^sin(x^2+根号x),求dy

y=e^sin(x^2+根号x),求dy

y'=[e^sin(x²+√x)]'
=e^sin(x²+√x)×[sin(x²+√x)]'
=e^sin(x²+√x)×cos(x²+√x)×(x²+√x)'
=cos(x²+√x)e^sin(x²+√x)×[2x+1/(2√x)]
=[2x+1/(2√x)]cos(x²+√x)e^sin(x²+√x)
∴dy={[2x+1/(2√x)]cos(x²+√x)e^sin(x²+√x)}dx