Solve 25x^2-40x+16-x^2+6x+7

$$25 x ^ { 2 } - 40 x + 16 - x ^ { 2 } + 6 x + 7$$

Evaluate

$$24x^{2}-34x+23$$

Solution Steps

Combine 25x^{2} and -x^{2} to get 24x^{2}.

$$24x^{2}-40x+16+6x+7$$

Combine -40x and 6x to get -34x.

$$24x^{2}-34x+16+7$$

Add 16 and 7 to get 23.

$$24x^{2}-34x+23$$

Differentiate w.r.t. x

$$48x-34$$

Steps Using Derivative Rule for Sum

Combine 25x^{2} and -x^{2} to get 24x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{2}-40x+16+6x+7)$$

Combine -40x and 6x to get -34x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{2}-34x+16+7)$$

Add 16 and 7 to get 23.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{2}-34x+23)$$

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}.

$$2\times 24x^{2-1}-34x^{1-1}$$

Multiply 2 times 24.

$$48x^{2-1}-34x^{1-1}$$

Subtract 1 from 2.

$$48x^{1}-34x^{1-1}$$

Subtract 1 from 1.

$$48x^{1}-34x^{0}$$

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

$$48x-34x^{0}$$

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

$$48x-34$$