1) y'(x)=5x^3+3*e^3x+2^x*ln(2) y'(6)=1080+3*e^18+64ln(2)
2) y'(x)=(x'(x^3+1)-x(x^3+1)')/(x^3+1)^2=(x^3+1)-x(3x^2)/(x^3+1)^2=((x^3+1)-3x^3)/(x^3+1)^2=(1-2x^3)/(x^3+1)^2 y'(0)=(1-0)/(0+1)^2=1
3)y'(x)=5(x^3+4x)^4*(x^3+4x)'+1/(x*ln5)=5(x^3+4x)^4*(3x^2+4)+1/(x*ln5)
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Answers & Comments
1) y'(x)=5x^3+3*e^3x+2^x*ln(2) y'(6)=1080+3*e^18+64ln(2)
2) y'(x)=(x'(x^3+1)-x(x^3+1)')/(x^3+1)^2=(x^3+1)-x(3x^2)/(x^3+1)^2=((x^3+1)-3x^3)/(x^3+1)^2=(1-2x^3)/(x^3+1)^2 y'(0)=(1-0)/(0+1)^2=1
3)y'(x)=5(x^3+4x)^4*(x^3+4x)'+1/(x*ln5)=5(x^3+4x)^4*(3x^2+4)+1/(x*ln5)