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

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

Evaluate

$$5u-3$$

Solution Steps

Combine -2u^{2} and 2u^{2} to get 0.

$$u-3+4u$$

Combine u and 4u to get 5u.

$$5u-3$$

Differentiate w.r.t. u

$$5$$

Steps Using Derivative Rule for Sum

Combine -2u^{2} and 2u^{2} to get 0.

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

Combine u and 4u to get 5u.

$$\frac{\mathrm{d}}{\mathrm{d}u}(5u-3)$$

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}.

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

Subtract 1 from 1.

$$5u^{0}$$

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

$$5\times 1$$

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

$$5$$