Solve 31x^2+3x-4+-8x^2-7x+6

$$31 { x }^{ 2 } +3x-4+-8 { x }^{ 2 } -7x+6$$

Evaluate

$$23x^{2}-4x+2$$

Solution Steps

Combine 31x^{2} and -8x^{2} to get 23x^{2}.

$$23x^{2}+3x-4-7x+6$$

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

$$23x^{2}-4x-4+6$$

Add -4 and 6 to get 2.

$$23x^{2}-4x+2$$

Differentiate w.r.t. x

$$46x-4$$

Steps Using Derivative Rule for Sum

Combine 31x^{2} and -8x^{2} to get 23x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(23x^{2}+3x-4-7x+6)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(23x^{2}-4x-4+6)$$

Add -4 and 6 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(23x^{2}-4x+2)$$

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}.

$$2\times 23x^{2-1}-4x^{1-1}$$

Multiply 2 times 23.

$$46x^{2-1}-4x^{1-1}$$

Subtract 1 from 2.

$$46x^{1}-4x^{1-1}$$

Subtract 1 from 1.

$$46x^{1}-4x^{0}$$

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

$$46x-4x^{0}$$

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

$$46x-4$$