Solve (5x^2-4x+3)+(2x-8x^2-9)

$$( 5 x ^ { 2 } - 4 x + 3 ) + ( 2 x - 8 x ^ { 2 } - 9 )$$

Evaluate

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

Solution Steps

Combine -4x and 2x to get -2x.

$$5x^{2}-2x+3-8x^{2}-9$$

Combine 5x^{2} and -8x^{2} to get -3x^{2}.

$$-3x^{2}-2x+3-9$$

Subtract 9 from 3 to get -6.

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

Differentiate w.r.t. x

$$-6x-2$$

Steps Using Derivative Rule for Sum

Combine -4x and 2x to get -2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-2x+3-8x^{2}-9)$$

Combine 5x^{2} and -8x^{2} to get -3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2}-2x+3-9)$$

Subtract 9 from 3 to get -6.

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

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}.

$$2\left(-3\right)x^{2-1}-2x^{1-1}$$

Multiply 2 times -3.

$$-6x^{2-1}-2x^{1-1}$$

Subtract 1 from 2.

$$-6x^{1}-2x^{1-1}$$

Subtract 1 from 1.

$$-6x^{1}-2x^{0}$$

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

$$-6x-2x^{0}$$

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

$$-6x-2$$