Question 1187926
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These problems are all on the same subject; but they are distinct problems and need to be submitted separately.<br>
I will do the first....<br>
{{{f(x) = (3x-4) (4x^3 - x^2 + 1)}}}<br>
This function is the product of two expressions, so one method is to use the product rule:<br>
{{{(d/dx)(f(x))=(d/dx)((a(x)*b(x)))=a*(db/dx)+b*(da/dx)}}}<br>
{{{(3x-4)(12x^2-2x)+3(4x^3-x^2+1)}}}
{{{(36x^3-54x^2+8x)+(12x^3-3x^2+3)}}}
{{{48x^3-57x^2+8x+3}}}<br>
Another option that in this case is easier, since it avoids use of the product rule, is to perform the indicated multiplication before taking the derivative.<br>
{{{f(x)=(3x-4) (4x^3 - x^2 + 1)}}}
{{{f(x)=12x^4-19x^3+4x^2+3x-4}}}
{{{df/dx=48x^3-57x^2+8x+3}}}<br>
Post the other problems separately....<br>