Solve (7u^2-5u+3)+(-u^2+2u+4)

$$( 7 u ^ { 2 } - 5 u + 3 ) + ( - u ^ { 2 } + 2 u + 4 )$$

Evaluate

$$6u^{2}-3u+7$$

Solution Steps

Combine -5u and 2u to get -3u.

$$7u^{2}-3u+3-u^{2}+4$$

Add 3 and 4 to get 7.

$$7u^{2}-3u+7-u^{2}$$

Combine 7u^{2} and -u^{2} to get 6u^{2}.

$$6u^{2}-3u+7$$

Differentiate w.r.t. u

$$12u-3$$

Steps Using Derivative Rule for Sum

Combine -5u and 2u to get -3u.

$$\frac{\mathrm{d}}{\mathrm{d}u}(7u^{2}-3u+3-u^{2}+4)$$

Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}u}(7u^{2}-3u+7-u^{2})$$

Combine 7u^{2} and -u^{2} to get 6u^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(6u^{2}-3u+7)$$

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}.

$$2\times 6u^{2-1}-3u^{1-1}$$

Multiply 2 times 6.

$$12u^{2-1}-3u^{1-1}$$

Subtract 1 from 2.

$$12u^{1}-3u^{1-1}$$

Subtract 1 from 1.

$$12u^{1}-3u^{0}$$

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

$$12u-3u^{0}$$

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

$$12u-3$$