Solve 3y+y^2-6y^2+7-4y+3y-2y-1

$$3 y + y ^ { 2 } - 6 y ^ { 2 } + 7 - 4 y + 3 y - 2 y - 1$$

Evaluate

$$6-5y^{2}$$

Solution Steps

Combine y^{2} and -6y^{2} to get -5y^{2}.

$$3y-5y^{2}+7-4y+3y-2y-1$$

Combine 3y and -4y to get -y.

$$-y-5y^{2}+7+3y-2y-1$$

Combine -y and 3y to get 2y.

$$2y-5y^{2}+7-2y-1$$

Combine 2y and -2y to get 0.

$$-5y^{2}+7-1$$

Subtract 1 from 7 to get 6.

$$-5y^{2}+6$$

Differentiate w.r.t. y

$$-10y$$

Steps Using Derivative Rule for Sum

Combine y^{2} and -6y^{2} to get -5y^{2}.

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

Combine 3y and -4y to get -y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-y-5y^{2}+7+3y-2y-1)$$

Combine -y and 3y to get 2y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y-5y^{2}+7-2y-1)$$

Combine 2y and -2y to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-5y^{2}+7-1)$$

Subtract 1 from 7 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-5y^{2}+6)$$

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}.

$$2\left(-5\right)y^{2-1}$$

Multiply 2 times -5.

$$-10y^{2-1}$$

Subtract 1 from 2.

$$-10y^{1}$$

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

$$-10y$$