Solve 12x^2-7x+9--3x^2+5x+13

$$12 { x }^{ 2 } -7x+9--3 { x }^{ 2 } +5x+13$$

Evaluate

$$15x^{2}-2x+22$$

Solution Steps

The opposite of -3x^{2} is 3x^{2}.

$$12x^{2}-7x+9+3x^{2}+5x+13$$

Combine 12x^{2} and 3x^{2} to get 15x^{2}.

$$15x^{2}-7x+9+5x+13$$

Combine -7x and 5x to get -2x.

$$15x^{2}-2x+9+13$$

Add 9 and 13 to get 22.

$$15x^{2}-2x+22$$

Differentiate w.r.t. x

$$30x-2$$

Steps Using Derivative Rule for Sum

The opposite of -3x^{2} is 3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}-7x+9+3x^{2}+5x+13)$$

Combine 12x^{2} and 3x^{2} to get 15x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{2}-7x+9+5x+13)$$

Combine -7x and 5x to get -2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{2}-2x+9+13)$$

Add 9 and 13 to get 22.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{2}-2x+22)$$

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}.

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

Multiply 2 times 15.

$$30x^{2-1}-2x^{1-1}$$

Subtract 1 from 2.

$$30x^{1}-2x^{1-1}$$

Subtract 1 from 1.

$$30x^{1}-2x^{0}$$

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

$$30x-2x^{0}$$

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

$$30x-2$$