Solve (2n^2+15)+(5n^2-2)

$$( 2 n ^ { 2 } + 15 ) + ( 5 n ^ { 2 } - 2 )$$

Evaluate

$$7n^{2}+13$$

Solution Steps

Combine 2n^{2} and 5n^{2} to get 7n^{2}.

$$7n^{2}+15-2$$

Subtract 2 from 15 to get 13.

$$7n^{2}+13$$

Differentiate w.r.t. n

$$14n$$

Steps Using Derivative Rule for Sum

Combine 2n^{2} and 5n^{2} to get 7n^{2}.

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

Subtract 2 from 15 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}n}(7n^{2}+13)$$

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}.

$$2\times 7n^{2-1}$$

Multiply 2 times 7.

$$14n^{2-1}$$

Subtract 1 from 2.

$$14n^{1}$$

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

$$14n$$