esercizi derivate 6

$y=(x+1)(x-1)(3x+4)=(x^2-1)(3x+4)=3x^3+4x^2-3x-4 \rightarrow y'=9x^2+8x-3$

$y=x(logx-1) \rightarrow y'=logx-1+x* \frac 1 x=logx-1+1=logx$

$y=e^x logx \rightarrow y= e^x logx + \frac {e^x}{x}=e^x (logx +\frac 1 x)$

$y=x^3logx \rightarrow y'=3x^2logx + x^3 \frac 1 x=3x^2logx+x^2=x^2(3logx+1)$

$y=x^4e^x \rightarrow y'=4x^3e^x+x^4e^x=x^3e^x(4+x)$

$y=e^x(x^2-3x+2) \rightarrow y'=e^x(x^2-3x+2)+e^x(2x-3)=e^x(x^2-x-1)$

$y=e^x(2-x^3) \rightarrow y'=e^x(2-x^3)+e^x(-3x^2)=-e^x(x^3+3x^2-2)$

$y=x logx -2x+1 \rightarrow y'=logx + x*\frac{1}{x} -2=logx+1-2=logx-1$

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