Solve (-ay^2-y)+(2ay^2-y+7)+10y

$$( - a y ^ { 2 } - y ) + ( 2 a y ^ { 2 } - y + 7 ) + 10 y$$

Differentiate w.r.t. y

$$2\left(ay+4\right)$$

Steps Using Derivative Rule for Sum

Combine -y and -y to get -2y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-a\right)y^{2}-2y+2ay^{2}+7+10y)$$

Combine -2y and 10y to get 8y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-a\right)y^{2}+8y+2ay^{2}+7)$$

Combine -ay^{2} and 2ay^{2} to get ay^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(ay^{2}+8y+7)$$

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}.

$$2ay^{2-1}+8y^{1-1}$$

Subtract 1 from 2.

$$2ay^{1}+8y^{1-1}$$

Subtract 1 from 1.

$$2ay^{1}+8y^{0}$$

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

$$2ay+8y^{0}$$

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

$$2ay+8\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2ay+8$$

Evaluate

$$ay^{2}+8y+7$$