Question: Note: in the following problem I am introducing a new notation for base e exponential function. The customary notation isex, but sometimes the exponent is

Note: in the following problem I am introducing a new notation for base e exponential function. The customary notation isex, but sometimes the exponent is complicated and it's easier to write exp(x).,exp(x)=ex For example, in statistics we often encounter the function f(x,,)=122e-(x-)222we can write this function as: ,f(x,,)=122exp(-(x-)222) and it may be a bit easier to interpret. In the following four examples of partial differentiation, three are correct and one is incorrect. Which of the statements is incorrect? adeldelx(1ye-x2y2)=deldelx(1yexp(-x2y2))=-2xy3e-x2y2=-2xy3exp(-x2y2)bdeldely(1ye-x2y2)=deldely(1yexp(-x2y2))=2x2y4e-x2y2-1y2e-x2y2=1y2(2x2y2-1)exp(-x2y2)cdeldel(sin()+Ln(2+))=12+*cos()ddeldelx(xyLn(ycos(x)))=y*Ln(ycos(x))-xy*tan(x)bdeldely(1ye-x2y2)=deldely(1yexp(-x2y2))=2x2y4e-x2y2-1y2e-x2y2=1y2(2x2y2-1)exp(-x2y2)is incorrectadeldelx(1ye-x2y2)=deldelx(1yexp(-x2y2))=-2xy3e-x2y2=-2xy3exp(-x2y2)is incorrectddeldelx(xyLn(ycos(x)))=y*Ln(ycos(x))-xy*tan(x)is incorrectcdeldel(sin()+Ln(2+))=12+*cos()is incorrect

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