Solve {l}{4-6y^{5}+y^{2}+7y^{3}-8y-y^{2}-6-3y^{4}-y^6-8y^3+19+9y^3}{-7y^2+y-5}

$$\left. \begin{array} { l } { 4 - 6 y ^ { 5 } + y ^ { 2 } + 7 y ^ { 3 } - 8 y - y ^ { 2 } - 6 - 3 y ^ { 4 } - y ^ { 6 } - 8 y ^ { 3 } + 19 + 9 y ^ { 3 } } \\ { - 7 y ^ { 2 } + y - 5 } \end{array} \right.$$

Evaluate

$$12-7y-7y^{2}+8y^{3}-3y^{4}-6y^{5}-y^{6}$$

Solution Steps

Combine y^{2} and -y^{2} to get 0.

$$4-6y^{5}+7y^{3}-8y-6-3y^{4}-y^{6}-8y^{3}+19+9y^{3}-7y^{2}+y-5$$

Subtract 6 from 4 to get -2.

$$-2-6y^{5}+7y^{3}-8y-3y^{4}-y^{6}-8y^{3}+19+9y^{3}-7y^{2}+y-5$$

Combine 7y^{3} and -8y^{3} to get -y^{3}.

$$-2-6y^{5}-y^{3}-8y-3y^{4}-y^{6}+19+9y^{3}-7y^{2}+y-5$$

Add -2 and 19 to get 17.

$$17-6y^{5}-y^{3}-8y-3y^{4}-y^{6}+9y^{3}-7y^{2}+y-5$$

Combine -y^{3} and 9y^{3} to get 8y^{3}.

$$17-6y^{5}+8y^{3}-8y-3y^{4}-y^{6}-7y^{2}+y-5$$

Combine -8y and y to get -7y.

$$17-6y^{5}+8y^{3}-7y-3y^{4}-y^{6}-7y^{2}-5$$

Subtract 5 from 17 to get 12.

$$12-6y^{5}+8y^{3}-7y-3y^{4}-y^{6}-7y^{2}$$

Differentiate w.r.t. y

$$-6y^{5}-30y^{4}-12y^{3}+24y^{2}-14y-7$$