Solve +2-(-9)-(-8y-(-8)=

$$+ 2 - ( - 9 ) - ( - 8 y - ( - 8 ) =$$

Evaluate

$$8y+3$$

Solution Steps

The opposite of -9 is 9.

$$2+9-\left(-8y-\left(-8\right)\right)$$

Add 2 and 9 to get 11.

$$11-\left(-8y-\left(-8\right)\right)$$

The opposite of -8 is 8.

$$11-\left(-8y+8\right)$$

To find the opposite of -8y+8, find the opposite of each term.

$$11-\left(-8y\right)-8$$

The opposite of -8y is 8y.

$$11+8y-8$$

Subtract 8 from 11 to get 3.

$$3+8y$$

Differentiate w.r.t. y

$$8$$

Steps Using Derivative Rule for Sum

The opposite of -9 is 9.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2+9-\left(-8y-\left(-8\right)\right))$$

Add 2 and 9 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}y}(11-\left(-8y-\left(-8\right)\right))$$

The opposite of -8 is 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(11-\left(-8y+8\right))$$

To find the opposite of -8y+8, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}y}(11-\left(-8y\right)-8)$$

The opposite of -8y is 8y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(11+8y-8)$$

Subtract 8 from 11 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3+8y)$$

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}.

$$8y^{1-1}$$

Subtract 1 from 1.

$$8y^{0}$$

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

$$8\times 1$$

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

$$8$$