Solve x^3+3x^2+x+3-x^3-4x^2-x+4/

$${ x }^{ 3 } +3 { x }^{ 2 } +x+3- { x }^{ 3 } -4 { x }^{ 2 } -x+ \frac{ 4 }{ }$$

Evaluate

$$7-x^{2}$$

Solution Steps

Combine x^{3} and -x^{3} to get 0.

$$3x^{2}+x+3-4x^{2}-x+\frac{4}{1}$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}+x+3-x+\frac{4}{1}$$

Combine x and -x to get 0.

$$-x^{2}+3+\frac{4}{1}$$

Anything divided by one gives itself.

$$-x^{2}+3+4$$

Add 3 and 4 to get 7.

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

Differentiate w.r.t. x

$$-2x$$

Steps Using Derivative Rule for Sum

Combine x^{3} and -x^{3} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+x+3-4x^{2}-x+\frac{4}{1})$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+x+3-x+\frac{4}{1})$$

Combine x and -x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+3+\frac{4}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+3+4)$$

Add 3 and 4 to get 7.

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

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}.

$$2\left(-1\right)x^{2-1}$$

Multiply 2 times -1.

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

Subtract 1 from 2.

$$-2x^{1}$$

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

$$-2x$$