Solve (-11n^2-8n+21)+(4n^2+15n-3)+(7n^2-10)

$$( - 11 n ^ { 2 } - 8 n + 21 ) + ( 4 n ^ { 2 } + 15 n - 3 ) + ( 7 n ^ { 2 } - 10 )$$

Evaluate

$$7n+8$$

Solution Steps

Combine -11n^{2} and 4n^{2} to get -7n^{2}.

$$-7n^{2}-8n+21+15n-3+7n^{2}-10$$

Combine -8n and 15n to get 7n.

$$-7n^{2}+7n+21-3+7n^{2}-10$$

Subtract 3 from 21 to get 18.

$$-7n^{2}+7n+18+7n^{2}-10$$

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

$$7n+18-10$$

Subtract 10 from 18 to get 8.

$$7n+8$$

Differentiate w.r.t. n

$$7$$

Steps Using Derivative Rule for Sum

Combine -11n^{2} and 4n^{2} to get -7n^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-7n^{2}-8n+21+15n-3+7n^{2}-10)$$

Combine -8n and 15n to get 7n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-7n^{2}+7n+21-3+7n^{2}-10)$$

Subtract 3 from 21 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-7n^{2}+7n+18+7n^{2}-10)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(7n+18-10)$$

Subtract 10 from 18 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}n}(7n+8)$$

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}.

$$7n^{1-1}$$

Subtract 1 from 1.

$$7n^{0}$$

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

$$7\times 1$$

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

$$7$$