Solve 8x+x^3-8+3x+4x-12

$$8 x + x ^ { 3 } - 8 + 3 x + 4 x - 12$$

Evaluate

$$x^{3}+15x-20$$

Solution Steps

Combine 8x and 3x to get 11x.

$$11x+x^{3}-8+4x-12$$

Combine 11x and 4x to get 15x.

$$15x+x^{3}-8-12$$

Subtract 12 from -8 to get -20.

$$15x+x^{3}-20$$

Differentiate w.r.t. x

$$3\left(x^{2}+5\right)$$

Steps Using Derivative Rule for Sum

Combine 8x and 3x to get 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x+x^{3}-8+4x-12)$$

Combine 11x and 4x to get 15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x+x^{3}-8-12)$$

Subtract 12 from -8 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x+x^{3}-20)$$

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}.

$$15x^{1-1}+3x^{3-1}$$

Subtract 1 from 1.

$$15x^{0}+3x^{3-1}$$

Subtract 1 from 3.

$$15x^{0}+3x^{2}$$

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

$$15\times 1+3x^{2}$$

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

$$15+3x^{2}$$