Solve (7x^3+2x^2-14x)+(-3x^3-2x^2+4x-3)

$$( 7 x ^ { 3 } + 2 x ^ { 2 } - 14 x ) + ( - 3 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 3 )$$

Evaluate

$$4x^{3}-10x-3$$

Solution Steps

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

$$4x^{3}+2x^{2}-14x-2x^{2}+4x-3$$

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

$$4x^{3}-14x+4x-3$$

Combine -14x and 4x to get -10x.

$$4x^{3}-10x-3$$

Differentiate w.r.t. x

$$12x^{2}-10$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}+2x^{2}-14x-2x^{2}+4x-3)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}-14x+4x-3)$$

Combine -14x and 4x to get -10x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}-10x-3)$$

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}.

$$3\times 4x^{3-1}-10x^{1-1}$$

Multiply 3 times 4.

$$12x^{3-1}-10x^{1-1}$$

Subtract 1 from 3.

$$12x^{2}-10x^{1-1}$$

Subtract 1 from 1.

$$12x^{2}-10x^{0}$$

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

$$12x^{2}-10$$