Solve 2-4y-6x^2-x^2+y+7x^2-2

$$2 - 4 y - 6 x ^ { 2 } - x ^ { 2 } + y + 7 x ^ { 2 } - 2$$

Evaluate

$$-3y$$

Solution Steps

Combine -6x^{2} and -x^{2} to get -7x^{2}.

$$2-4y-7x^{2}+y+7x^{2}-2$$

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

$$2-3y-7x^{2}+7x^{2}-2$$

Combine -7x^{2} and 7x^{2} to get 0.

$$2-3y-2$$

Subtract 2 from 2 to get 0.

$$-3y$$

Differentiate w.r.t. y

$$-3$$

Steps Using Definition of a Derivative

Combine -6x^{2} and -x^{2} to get -7x^{2}.

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

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

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

Combine -7x^{2} and 7x^{2} to get 0.

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

Subtract 2 from 2 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-3y)$$

The derivative of ax^{n} is nax^{n-1}.

$$-3y^{1-1}$$

Subtract 1 from 1.

$$-3y^{0}$$

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

$$-3$$