$$(3y^{5}-4y^{3}+y^{2}+y-7)+(-3y^{5}+4y^{3}+6y^{2}+7+2)$$
$7y^{2}+y+2$
$$-4y^{3}+y^{2}+y-7+4y^{3}+6y^{2}+7+2$$
$$y^{2}+y-7+6y^{2}+7+2$$
$$7y^{2}+y-7+7+2$$
$$7y^{2}+y+2$$
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$14y+1$
$$\frac{\mathrm{d}}{\mathrm{d}y}(-4y^{3}+y^{2}+y-7+4y^{3}+6y^{2}+7+2)$$
$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{2}+y-7+6y^{2}+7+2)$$
$$\frac{\mathrm{d}}{\mathrm{d}y}(7y^{2}+y-7+7+2)$$
$$\frac{\mathrm{d}}{\mathrm{d}y}(7y^{2}+y+2)$$
$$2\times 7y^{2-1}+y^{1-1}$$
$$14y^{2-1}+y^{1-1}$$
$$14y^{1}+y^{1-1}$$
$$14y^{1}+y^{0}$$
$$14y+y^{0}$$
$$14y+1$$
