1.f(x)=x(x^2+1/x+1/x^3) 2.f(x)=(e^x+Inx)/x 3.f(x)=sinx(cosx+2^x) _数学解答

1.f(x)=x(x^2+1/x+1/x^3) 2.f(x)=(e^x+Inx)/x 3.f(x)=sinx(cosx+2^x) 4.f(x)=5log2(2x+1)

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解答

1.f(x)=x(x^2+1/x+1/x^3) =x^3+1+1/x^3f'(x)=3x^2-(1/3)/x^42.f(x)=(e^x+Inx)/xf'(x)=[(e^x+Inx)'+(e^x+Inx)x]/x^2 =(e^x+1/x+xe^x+xInx)/x^2=(x^2*e^x+xe^x+x^2*lnx+1)/x^#3.f(x)=sinx(cosx+2^x) f'(x)= (sinx)'(co...