Solve (2x^2-8x+16)+(x+4)

$$( 2 x ^ { 2 } - 8 x + 16 ) + ( x + 4 )$$

Evaluate

$$2x^{2}-7x+20$$

Solution Steps

Combine -8x and x to get -7x.

$$2x^{2}-7x+16+4$$

Add 16 and 4 to get 20.

$$2x^{2}-7x+20$$

Differentiate w.r.t. x

$$4x-7$$

Steps Using Derivative Rule for Sum

Combine -8x and x to get -7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-7x+16+4)$$

Add 16 and 4 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-7x+20)$$

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}.

$$2\times 2x^{2-1}-7x^{1-1}$$

Multiply 2 times 2.

$$4x^{2-1}-7x^{1-1}$$

Subtract 1 from 2.

$$4x^{1}-7x^{1-1}$$

Subtract 1 from 1.

$$4x^{1}-7x^{0}$$

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

$$4x-7x^{0}$$

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

$$4x-7$$