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

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

Evaluate

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

Solution Steps

Combine -2u^{2} and 7u^{2} to get 5u^{2}.

$$5u^{2}+3u-4+u+5$$

Combine 3u and u to get 4u.

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

Add -4 and 5 to get 1.

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

Differentiate w.r.t. u

$$10u+4$$

Steps Using Derivative Rule for Sum

Combine -2u^{2} and 7u^{2} to get 5u^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(5u^{2}+3u-4+u+5)$$

Combine 3u and u to get 4u.

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

Add -4 and 5 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}u}(5u^{2}+4u+1)$$

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}.

$$2\times 5u^{2-1}+4u^{1-1}$$

Multiply 2 times 5.

$$10u^{2-1}+4u^{1-1}$$

Subtract 1 from 2.

$$10u^{1}+4u^{1-1}$$

Subtract 1 from 1.

$$10u^{1}+4u^{0}$$

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

$$10u+4u^{0}$$

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

$$10u+4\times 1$$

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

$$10u+4$$