Solve (5u^2-7u+6)+(-3u^2+2u+4)

$$( 5 u ^ { 2 } - 7 u + 6 ) + ( - 3 u ^ { 2 } + 2 u + 4 )$$

Evaluate

$$2u^{2}-5u+10$$

Solution Steps

Combine 5u^{2} and -3u^{2} to get 2u^{2}.

$$2u^{2}-7u+6+2u+4$$

Combine -7u and 2u to get -5u.

$$2u^{2}-5u+6+4$$

Add 6 and 4 to get 10.

$$2u^{2}-5u+10$$

Differentiate w.r.t. u

$$4u-5$$

Steps Using Derivative Rule for Sum

Combine 5u^{2} and -3u^{2} to get 2u^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(2u^{2}-7u+6+2u+4)$$

Combine -7u and 2u to get -5u.

$$\frac{\mathrm{d}}{\mathrm{d}u}(2u^{2}-5u+6+4)$$

Add 6 and 4 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}u}(2u^{2}-5u+10)$$

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}.

$$2\times 2u^{2-1}-5u^{1-1}$$

Multiply 2 times 2.

$$4u^{2-1}-5u^{1-1}$$

Subtract 1 from 2.

$$4u^{1}-5u^{1-1}$$

Subtract 1 from 1.

$$4u^{1}-5u^{0}$$

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

$$4u-5u^{0}$$

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

$$4u-5$$