Question 1003759
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(a)  {{{f(x)=(x^2+1/x^3 )(x^3-x^2+1)}}}

Write {{{1/x^3}}} as {{{x^(-3)}}}

{{{f(x)=(x^2+x^(-3) )(x^3-x^2+1)}}}

Multiply it out first:

{{{f(x)=(x^2+x^(-3) )(x^3-x^2+1)}}}

{{{f(x)=x^5-x^4+x^2+x^0-x^(-1)+x^(-3)}}}

{{{f(x)=x^5-x^4+x^2+1-x^(-1)+x^(-3)}}}

Take the derivative of each term:

{{{"f'(x)"=5x^4-4x^3+2x+x^(-2)-3x^(-4)}}}

Changing negative exponents to
positive exponents in denominators.

{{{"f'(x)"= 5x^4-4x^3+2x+1/x^2-3/x^4}}}

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(b)  {{{matrix(2,1,"",f(x)= e^(x^3+2x))}}}

Rule:  copy it over and multiply by the derivative of the exponent:

{{{matrix(2,1,"","f'(x)"= e^(x^3+2x)*(3x^2+2))}}}

Edwin</pre>