Solve (4-8x+4x^2)+(8-7x+6x^2)

$$( 4 - 8 x + 4 x ^ { 2 } ) + ( 8 - 7 x + 6 x ^ { 2 } )$$

Evaluate

$$10x^{2}-15x+12$$

Solution Steps

Add 4 and 8 to get 12.

$$12-8x+4x^{2}-7x+6x^{2}$$

Combine -8x and -7x to get -15x.

$$12-15x+4x^{2}+6x^{2}$$

Combine 4x^{2} and 6x^{2} to get 10x^{2}.

$$12-15x+10x^{2}$$

Differentiate w.r.t. x

$$20x-15$$

Steps Using Derivative Rule for Sum

Add 4 and 8 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12-8x+4x^{2}-7x+6x^{2})$$

Combine -8x and -7x to get -15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12-15x+4x^{2}+6x^{2})$$

Combine 4x^{2} and 6x^{2} to get 10x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12-15x+10x^{2})$$

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}.

$$-15x^{1-1}+2\times 10x^{2-1}$$

Subtract 1 from 1.

$$-15x^{0}+2\times 10x^{2-1}$$

Multiply 2 times 10.

$$-15x^{0}+20x^{2-1}$$

Subtract 1 from 2.

$$-15x^{0}+20x^{1}$$

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

$$-15x^{0}+20x$$

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

$$-15+20x$$