Solve x^2-7x+4+x^2+4x+6=

$$x ^ { 2 } - 7 x + 4 + x ^ { 2 } + 4 x + 6 =$$

Evaluate

$$2x^{2}-3x+10$$

Solution Steps

Combine x^{2} and x^{2} to get 2x^{2}.

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

Combine -7x and 4x to get -3x.

$$2x^{2}-3x+4+6$$

Add 4 and 6 to get 10.

$$2x^{2}-3x+10$$

Differentiate w.r.t. x

$$4x-3$$

Steps Using Derivative Rule for Sum

Combine x^{2} and x^{2} to get 2x^{2}.

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

Combine -7x and 4x to get -3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-3x+4+6)$$

Add 4 and 6 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-3x+10)$$

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}.

$$2\times 2x^{2-1}-3x^{1-1}$$

Multiply 2 times 2.

$$4x^{2-1}-3x^{1-1}$$

Subtract 1 from 2.

$$4x^{1}-3x^{1-1}$$

Subtract 1 from 1.

$$4x^{1}-3x^{0}$$

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

$$4x-3x^{0}$$

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

$$4x-3$$