f(x)=x^2*sinx*cosx,求f(2013阶导数)(0)

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f(x)=x^2*sinx*cosx,求f(2013阶导数)(0)f(x)=x^2*sinx*cosx,求f(2013阶导数)(0)f(x)=x^2*sinx*cosx,求f(2013阶导数)(0)f

f(x)=x^2*sinx*cosx,求f(2013阶导数)(0)
f(x)=x^2*sinx*cosx,求f(2013阶导数)(0)

f(x)=x^2*sinx*cosx,求f(2013阶导数)(0)
f(x)=x^2*sinx*cosx=(1/2)x^2*sin2x
用莱布尼兹高阶导数公式:
f^(2013)= (1/2)x^2(sin2x)^(2013)+(1/2)(2013)2x(sin2x)^(2012)+ (1/2)(2013)(2012)(sin2x)^(2011)
前两项代x=0时为0,而(sin2x)^(2011)=2^(2011)sin(2x+2011π/2)
所以:f^(2013)(0)=-(2013)*(2012)2^(2010)