Solve 4x^3-2x^2+x-1--3x^3+4x^2-x-2

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

Evaluate

$$7x^{3}+2x^{2}-3$$

Solution Steps

The opposite of -3x^{3} is 3x^{3}.

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

Combine 4x^{3} and 3x^{3} to get 7x^{3}.

$$7x^{3}-2x^{2}+x-1+4x^{2}-x-2$$

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

$$7x^{3}+2x^{2}+x-1-x-2$$

Combine x and -x to get 0.

$$7x^{3}+2x^{2}-1-2$$

Subtract 2 from -1 to get -3.

$$7x^{3}+2x^{2}-3$$

Differentiate w.r.t. x

$$x\left(21x+4\right)$$

Steps Using Derivative Rule for Sum

The opposite of -3x^{3} is 3x^{3}.

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

Combine 4x^{3} and 3x^{3} to get 7x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}-2x^{2}+x-1+4x^{2}-x-2)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}+2x^{2}+x-1-x-2)$$

Combine x and -x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}+2x^{2}-1-2)$$

Subtract 2 from -1 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}+2x^{2}-3)$$

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}.

$$3\times 7x^{3-1}+2\times 2x^{2-1}$$

Multiply 3 times 7.

$$21x^{3-1}+2\times 2x^{2-1}$$

Subtract 1 from 3.

$$21x^{2}+2\times 2x^{2-1}$$

Multiply 2 times 2.

$$21x^{2}+4x^{2-1}$$

Subtract 1 from 2.

$$21x^{2}+4x^{1}$$

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

$$21x^{2}+4x$$