Solve (2x^2-6)+(5x^2+2)+(-x^2-7)

$$( 2 x ^ { 2 } - 6 ) + ( 5 x ^ { 2 } + 2 ) + ( - x ^ { 2 } - 7 )$$

Evaluate

$$6x^{2}-11$$

Solution Steps

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

$$7x^{2}-6+2-x^{2}-7$$

Add -6 and 2 to get -4.

$$7x^{2}-4-x^{2}-7$$

Subtract 7 from -4 to get -11.

$$7x^{2}-11-x^{2}$$

Combine 7x^{2} and -x^{2} to get 6x^{2}.

$$6x^{2}-11$$

Differentiate w.r.t. x

$$12x$$

Steps Using Derivative Rule for Sum

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

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

Add -6 and 2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-4-x^{2}-7)$$

Subtract 7 from -4 to get -11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-11-x^{2})$$

Combine 7x^{2} and -x^{2} to get 6x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}-11)$$

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}.

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

Multiply 2 times 6.

$$12x^{2-1}$$

Subtract 1 from 2.

$$12x^{1}$$

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

$$12x$$