Solve y^2-8y+9-6y^3+2y^2-y-11

$$y ^ { 2 } - 8 y + 9 - 6 y ^ { 3 } + 2 y ^ { 2 } - y - 11$$

Evaluate

$$-6y^{3}+3y^{2}-9y-2$$

Solution Steps

Combine y^{2} and 2y^{2} to get 3y^{2}.

$$3y^{2}-8y+9-6y^{3}-y-11$$

Combine -8y and -y to get -9y.

$$3y^{2}-9y+9-6y^{3}-11$$

Subtract 11 from 9 to get -2.

$$3y^{2}-9y-2-6y^{3}$$

Differentiate w.r.t. y

$$-18y^{2}+6y-9$$

Steps Using Derivative Rule for Sum

Combine y^{2} and 2y^{2} to get 3y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{2}-8y+9-6y^{3}-y-11)$$

Combine -8y and -y to get -9y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{2}-9y+9-6y^{3}-11)$$

Subtract 11 from 9 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{2}-9y-2-6y^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 3y^{2-1}-9y^{1-1}+3\left(-6\right)y^{3-1}$$

Multiply 2 times 3.

$$6y^{2-1}-9y^{1-1}+3\left(-6\right)y^{3-1}$$

Subtract 1 from 2.

$$6y^{1}-9y^{1-1}+3\left(-6\right)y^{3-1}$$

Subtract 1 from 1.

$$6y^{1}-9y^{0}+3\left(-6\right)y^{3-1}$$

Multiply 1 times -9.

$$6y^{1}-9y^{0}-18y^{3-1}$$

Subtract 1 from 3.

$$6y^{1}-9y^{0}-18y^{2}$$

For any term t, t^{1}=t.

$$6y-9y^{0}-18y^{2}$$

For any term t except 0, t^{0}=1.

$$6y-9-18y^{2}$$