Solve (12x^2+3x-3)+(-5x^2-3x+16)

$$(12 { x }^{ 2 } +3x-3)+(-5 { x }^{ 2 } -3x+16)$$

Evaluate

$$7x^{2}+13$$

Solution Steps

Combine 12x^{2} and -5x^{2} to get 7x^{2}.

$$7x^{2}+3x-3-3x+16$$

Combine 3x and -3x to get 0.

$$7x^{2}-3+16$$

Add -3 and 16 to get 13.

$$7x^{2}+13$$

Differentiate w.r.t. x

$$14x$$

Steps Using Derivative Rule for Sum

Combine 12x^{2} and -5x^{2} to get 7x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+3x-3-3x+16)$$

Combine 3x and -3x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-3+16)$$

Add -3 and 16 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+13)$$

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}.

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

Multiply 2 times 7.

$$14x^{2-1}$$

Subtract 1 from 2.

$$14x^{1}$$

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

$$14x$$