Find the derivative of the function.

yequals$=$StartFraction x squared minus $3$ x plus $2$ Over x Superscript $7$ Baseline minus $2$ EndFractionx$23$x$+2$x$72$

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Part $1$

A$.$y prime equals StartFraction negative $5$ x Superscript $8$ Baseline plus $19$ x Superscript $7$ Baseline minus $14$ x Superscript $6$ Baseline minus $4$ x plus $6$ Over left parenthesis x Superscript $7$ Baseline minus $2$ right parenthesis squared EndFraction

y primey$$equals$=$StartFraction negative $5$ x Superscript $8$ Baseline plus $19$ x Superscript $7$ Baseline minus $14$ x Superscript $6$ Baseline minus $4$ x plus $6$ Over left parenthesis x Superscript $7$ Baseline minus $2$ right parenthesis squared EndFraction$5$x$8+19$x$714$x$64$x$+6$x$722$

B$.$y prime equals StartFraction negative $5$ x Superscript $8$ Baseline plus $18$ x Superscript $7$ Baseline minus $14$ x Superscript $6$ Baseline minus $4$ x plus $6$ Over left parenthesis x Superscript $7$ Baseline minus $2$ right parenthesis squared EndFraction

y primey$$equals$=$StartFraction negative $5$ x Superscript $8$ Baseline plus $18$ x Superscript $7$ Baseline minus $14$ x Superscript $6$ Baseline minus $4$ x plus $6$ Over left parenthesis x Superscript $7$ Baseline minus $2$ right parenthesis squared EndFraction$5$x$8+18$x$714$x$64$x$+6$x$722$

C$.$y prime equals StartFraction negative $5$ x Superscript $8$ Baseline plus $18$ x Superscript $7$ Baseline minus $14$ x Superscript $6$ Baseline minus $3$ x plus $6$ Over left parenthesis x Superscript $7$ Baseline minus $2$ right parenthesis squared EndFraction

y primey$$equals$=$StartFraction negative $5$ x Superscript $8$ Baseline plus $18$ x Superscript $7$ Baseline minus $14$ x Superscript $6$ Baseline minus $3$ x plus $6$ Over left parenthesis x Superscript $7$ Baseline minus $2$ right parenthesis squared EndFraction$5$x$8+18$x$714$x$63$x$+6$x$722$

D$.$y prime equals StartFraction negative $5$ x Superscript $8$ Baseline plus $18$ x Superscript $7$ Baseline minus $13$ x Superscript $6$ Baseline minus $4$ x plus $6$ Over left parenthesis x Superscript $7$ Baseline minus $2$ right parenthesis squared EndFraction

y primey$$equals$=$StartFraction negative $5$ x Superscript $8$ Baseline plus $18$ x Superscript $7$ Baseline minus $13$ x Superscript $6$ Baseline minus $4$ x plus $6$ Over left parenthesis x Superscript $7$ Baseline minus $2$ right parenthesis squared EndFraction