y=e^sin(x^2+根号x),求dy

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y=e^sin(x^2+根号x),求dy
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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
解
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

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