Solve -x^2+8x+4,7-x-9,1+x^2=

$$- x ^ { 2 } + 8 x + 4,7 - x - 9,1 + x ^ { 2 } =$$

Evaluate

$$7x-4,4$$

Solution Steps

Combine 8x and -x to get 7x.

$$-x^{2}+7x+4,7-9,1+x^{2}$$

Subtract 9,1 from 4,7 to get -4,4.

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

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

$$7x-4,4$$

Differentiate w.r.t. x

$$7$$

Steps Using Derivative Rule for Sum

Combine 8x and -x to get 7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+7x+4,7-9,1+x^{2})$$

Subtract 9,1 from 4,7 to get -4,4.

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

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

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

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.

$$7$$