Solve (5+x^2-3x)+(x+2)

$$( 5 + x ^ { 2 } - 3 x ) + ( x + 2 )$$

Evaluate

$$x^{2}-2x+7$$

Solution Steps

Combine -3x and x to get -2x.

$$5+x^{2}-2x+2$$

Add 5 and 2 to get 7.

$$7+x^{2}-2x$$

Differentiate w.r.t. x

$$2\left(x-1\right)$$

Steps Using Derivative Rule for Sum

Combine -3x and x to get -2x.

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

Add 5 and 2 to get 7.

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

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}.

$$2x^{2-1}-2x^{1-1}$$

Subtract 1 from 2.

$$2x^{1}-2x^{1-1}$$

Subtract 1 from 1.

$$2x^{1}-2x^{0}$$

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

$$2x-2x^{0}$$

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

$$2x-2$$