Solve -x^2+8x+47-x-91+x^2=

$$- x ^ { 2 } + 8 x + 47 - x - 91 + x ^ { 2 } =$$

Evaluate

$$7x-44$$

Solution Steps

Combine 8x and -x to get 7x.

$$-x^{2}+7x+47-91+x^{2}$$

Subtract 91 from 47 to get -44.

$$-x^{2}+7x-44+x^{2}$$

Combine -x^{2} and x^{2} to get 0.

$$7x-44$$

Differentiate w.r.t. x

$$7$$

Steps Using Derivative Rule for Sum

Combine 8x and -x to get 7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+7x+47-91+x^{2})$$

Subtract 91 from 47 to get -44.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+7x-44+x^{2})$$

Combine -x^{2} and x^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x-44)$$

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}.

$$7x^{1-1}$$

Subtract 1 from 1.

$$7x^{0}$$

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

$$7\times 1$$

For any term t, t\times 1=t and 1t=t.

$$7$$