Solve (9y^2+y-9)+(6y^2-y-8)

$$( 9 y ^ { 2 } + y - 9 ) + ( 6 y ^ { 2 } - y - 8 )$$

Evaluate

$$15y^{2}-17$$

Solution Steps

Combine 9y^{2} and 6y^{2} to get 15y^{2}.

$$15y^{2}+y-9-y-8$$

Combine y and -y to get 0.

$$15y^{2}-9-8$$

Subtract 8 from -9 to get -17.

$$15y^{2}-17$$

Differentiate w.r.t. y

$$30y$$

Steps Using Derivative Rule for Sum

Combine 9y^{2} and 6y^{2} to get 15y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{2}+y-9-y-8)$$

Combine y and -y to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{2}-9-8)$$

Subtract 8 from -9 to get -17.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{2}-17)$$

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.

$$30y$$