Solve (8y^2+y-8)+(7y^2-y-5)

$$( 8 y ^ { 2 } + y - 8 ) + ( 7 y ^ { 2 } - y - 5 )$$

Evaluate

$$15y^{2}-13$$

Solution Steps

Combine 8y^{2} and 7y^{2} to get 15y^{2}.

$$15y^{2}+y-8-y-5$$

Combine y and -y to get 0.

$$15y^{2}-8-5$$

Subtract 5 from -8 to get -13.

$$15y^{2}-13$$

Differentiate w.r.t. y

$$30y$$

Steps Using Derivative Rule for Sum

Combine 8y^{2} and 7y^{2} to get 15y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{2}+y-8-y-5)$$

Combine y and -y to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{2}-8-5)$$

Subtract 5 from -8 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{2}-13)$$

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}.

$$2\times 15y^{2-1}$$

Multiply 2 times 15.

$$30y^{2-1}$$

Subtract 1 from 2.

$$30y^{1}$$

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

$$30y$$